Pang, Genny (2012). Experimental Determination of Rate Constants For

EXPERIMENTAL DETERMINATION OF RATE CONSTANTS FOR REACTIONS OF THE HYDROXYL RADICAL WITH ALKANES AND ALCOHOLS

A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

Genny Anne Pang August 2012

This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/rh393tq1232

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Ronald Hanson, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Craig Bowman

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

David Golden

Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.

iii iv Abstract

Over one quarter of the energy usage in the United States currently occurs in the transportation sector. Improvements in energy conversion eﬃciency and sustainability in transportation applications, therefore, can substantially contribute to improved energy security in our future. The design of advanced high-eﬃciency energy conversion devices for transportation applications can be facilitated with complex computer models of combustion processes. The development of these models requires a large experimental database to ensure accuracy of the computational predictions. This thesis discusses how experimental studies are utilized to create a database of rate constants for elementary reactions; these rate constants are integral components of any computational model of combustion chemistry.

During a combustion process, the reaction of the hydroxyl (OH) radical, a highly reactive chemical intermediate, with a combustible fuel molecule is a major fuel consumption pathway under many combustion conditions. Thus, the rate constants for these types of reactions must be accurately known to develop a computational model that correctly describes the combustion chemistry. This thesis presents an experimental method for measuring rate constants in the reaction family of OH + Fuel −→ Products using a shock tube reactor, laser diagnostics, and tert- butylhydroperoxide (TBHP) as an OH radical precursor. Important rate constant parameters describing subsequent reactions of TBHP decomposition are also studied.

Current transportation fuels of interest in the combustion community include molecules in the alkane and butanol classes. Alkane molecules are a major component of many petroleum-derived fuels such as gasoline and jet fuel. Isomers of the

v butanol molecule are gaining popularity as a potential renewable alternative to gasoline because of their high energy density and the many known methods of production from biomass and agricultural byproducts. The rate constant measurement method is applied to the reaction of OH with three alkane molecules (n-pentane, n-heptane, and n-nonane) and four isomers of butanol (n-butanol, iso-butanol, sec-butanol, tert- butanol), and the results are reported in this thesis. Comparison of the rate constant results to estimation methods in the literature are presented, and, for several of the isomers of butanol studied, the measured data are also used to validate and/or suggest reﬁnements to existing detailed kinetic mechanisms.

vi Acknowledgment

The work presented in this thesis would not have been possible without the extensive support provided by my primary advisor Prof. Ron Hanson. I thank him for having confidence in me when I was initially exploring my graduate school options, for without his encouragement I may not have spent my graduate studies working in his world-class laboratory. And I am thankful that his support for me has never faded throughout my time at Stanford. His constant push to strive for the best in quality of work and presentation has no doubt led me to be a become a better researcher, scholar, teacher, and mentor than I would have been without his guidance. I would also like to thank Profs. Tom Bowman and Dave Golden for being my reading committee members and weekly consultants for my work. Prof. Bowman’s meticulous attention to detail has taught me what high-quality research is, and also how to achieve it in my work. I thank Prof. Golden for teaching me to think like a chemist. The direction of this thesis work would not have been the same without his inspiration. I owe thanks to Profs. Jen Wilcox for chairing my oral exam, and also for teaching me about about topics that have increased my depth of understanding in this work. I am very thankful to Prof. Mark Cappelli for serving on my oral exam committee on short notice, and also being a supportive faculty member all throughout my graduate studies, starting from my very first class at Stanford. I also want to acknowledge support from Prof. Justin Du Bois. His patience and enthusiasm in teaching organic chemistry helped me develop a foundation to base many parts of this work, and I thank him for many interesting and insightful discussions in his office. I am immensely grateful for Dr. Dave Davidson’s presence in the laboratory, and

vii also in my life as a mentor, colleague, and friend. I am especially thankful for his willingness to always make time for students, whether by getting up from his desk to examine a laboratory problem with me, or just to provide wisdom, laughter, and chocolate during both good and difficult times. I also thank Dr. Jay Jeffries for his assistance in managing the laboratory and for helping me with occasional tasks. I feel fortunate to have worked with the extraordinary group of students in the Hanson Group. I particularly want to acknowledge the experimental assistance from Venky Vasudevan and Rob Cook. I thank them for their patience in teaching me to use the laser equipment and helping troubleshoot problems; the experimental work presented in this thesis would have been much more difficult without their help. I am grateful for the rest of my friends and colleagues from the Hanson Group, past and present, as my memories of group lunches, coffee breaks, ski trips, and other activities with the group will always be highlights of my time at Stanford. Perhaps most importantly, I am indebted to my friends, family, and loved ones outside of the laboratory who have made my experience in graduate school special. Their company and support has enriched my life in ways that I never would have imagined; and for that, I will be forever grateful.

Financial support for the specific research presented in this thesis was provided by the U.S. Department of Energy, Office of Basic Energy Sciences, with Dr. Wade Sisk as Program Manager. The National Defense Science and Engineering Graduate Fellowship, awarded by the Department of Defense, also provided tuition and stipend support for the early years of my graduate studies. Countless faculty, students, and affiliates of the Combustion Energy Frontier Research Center, funded by the U.S. Department of Energy, are also acknowledged for their support.

viii Contents

Abstract v

Acknowledgment vii

1 Introduction 1 1.1 Motivation ...... 1 1.2 Background ...... 2 1.2.1 Development of Kinetic Mechanisms for Combustion . . . . .2 1.2.2 Alkane Combustion Kinetics ...... 6 1.2.3 Butanol Combustion Kinetics ...... 8 1.3 Scope and Organization of Thesis ...... 10

2 Experimental Setup 13 2.1 Introduction ...... 13 2.2 Kinetics Shock Tube Facility ...... 13 2.2.1 Shock Tube Overview ...... 14 2.2.2 Gas-mixing Facility Overview ...... 17 2.3 Laser Diagnostics ...... 20 2.3.1 OH Mole-fraction Diagnostic ...... 20 2.3.2 Organic Fuel Mole Fraction Diagnostic ...... 24 2.4 Test Mixture Chemicals ...... 26

3 Decomposition of tert-Butylhydroperoxide 27 3.1 Introduction ...... 27

ix 3.1.1 Background ...... 27 3.1.2 Objectives of the Current Chapter ...... 29 3.2 TBHP Kinetic Mechanism ...... 30 3.2.1 Mechanism Generation ...... 30 3.2.2 OH Sensitivity Analysis ...... 31 3.3 Experimental ...... 32 3.4 OH Mole Fraction Measurements ...... 34 3.4.1 OH Time-history ...... 34 3.4.2 OH Yield ...... 35 3.5 Rate Constant Determinations ...... 38

3.5.1 Determination of k3.1 ...... 38

3.5.2 Determination of k3.3 ...... 41 3.6 Summary ...... 44

4 Reactions of OH with n-Alkanes 47 4.1 Introduction ...... 47 4.1.1 Background ...... 47 4.1.2 Objectives of the Current Chapter ...... 48 4.2 Experimental ...... 49 4.3 Data Analysis ...... 49 4.3.1 Pseudo-ﬁrst-order ...... 50 4.3.2 Kinetic Modeling ...... 51 4.4 Results ...... 54 4.4.1 Rate Constant Measurements ...... 54 4.4.2 Uncertainty Analysis ...... 59 4.5 Comparisons with Literature ...... 60 4.5.1 Previous Experimental Works ...... 60 4.5.2 Validation of Estimation Methods ...... 62 4.6 Conclusions ...... 66

5 Reaction of OH with n-Butanol 69 5.1 Introduction ...... 69

x 5.1.1 Background and Motivation ...... 69 5.1.2 Objectives of the Current Chapter ...... 71 5.2 Analysis of n-Butanol Kinetic Mechanisms ...... 72 5.2.1 Inﬂuence of TBHP Kinetics ...... 72

5.2.2 Sensitivity of k5.1 Determination to Mechanism ...... 75 5.2.3 Mechanism Generation for Current Work ...... 78 5.3 Experimental ...... 80 5.4 Results ...... 81 5.5 Inﬂuence of Secondary Reactions ...... 83 5.5.1 OH Sensitivity Analysis ...... 83 5.5.2 Reaction Pathway Analysis ...... 85 5.6 Uncertainty Estimation ...... 88 5.7 Comparison with Literature ...... 89 5.7.1 Previous Experiments at High Temperatures ...... 89 5.7.2 Ab initio Calculations ...... 93 5.7.3 Atmospheric-relevant Temperature Rate Constants ...... 94 5.8 Conclusions ...... 95

6 Reaction of OH with iso-Butanol 97 6.1 Introduction ...... 97 6.1.1 Background and Motivation ...... 97 6.1.2 Objectives of the Current Chapter ...... 99 6.2 Experimental ...... 100 6.3 Kinetic Modeling and Analysis ...... 100 6.3.1 Model Description ...... 100 6.3.2 OH Sensitivity Analysis ...... 103 6.4 Results and Discussion ...... 104 6.4.1 Rate Constant Measurements for the non-β Pathways . . . . . 104 6.4.2 Comparison to Rate Constant Recommendations ...... 107 6.5 Overall Rate Constant Recommendation ...... 109 6.6 Conclusions ...... 112

xi 7 Reaction of OH with sec-Butanol 113 7.1 Introduction ...... 113 7.1.1 Background and Motivation ...... 113 7.1.2 Objectives of the Current Chapter ...... 115 7.2 Experimental ...... 116 7.3 Secondary Reaction Pathway Modeling ...... 116 7.4 OH Time-histories and Rate Constant Determination ...... 120 7.5 Discussion ...... 123 7.5.1 Mechanism Performances ...... 123 7.5.2 Low-temperature Rate Constants ...... 124 7.6 Conclusions ...... 126

8 Reaction of OH with tert-Butanol 129 8.1 Introduction ...... 129 8.1.1 Background and Motivation ...... 129 8.1.2 Objectives of the Current Chapter ...... 132 8.1.3 Organization of this Chapter’s Results ...... 132 8.2 Experimental ...... 133 8.3 Net OH Removal Rates ...... 133 8.4 Kinetic Modeling ...... 135 8.4.1 Net OH Removal Rate by Reaction with tert-Butanol . . . . . 139 8.5 Branching Ratio Determinations ...... 142

8.5.1 Evaluation of brOH ...... 142

8.5.2 Evaluation of brβ ...... 142 8.6 Overall Rate Constant Determination ...... 145 8.6.1 Comparisons to Mechanism Predictions ...... 146 8.6.2 Comparisons to Low-temperature Literature ...... 148 8.7 Conclusions ...... 149

9 Concluding Remarks 151 9.1 Summary of Work ...... 151 9.2 Implications for Addressing Global Challenges ...... 156

xii 9.3 Recommendations for Future Work ...... 156 9.3.1 Alkane Combustion Kinetics ...... 156 9.3.2 Butanol Combustion Kinetics ...... 157

A Shock Tube Cleaning Techniques 161 A.1 Introduction ...... 161 A.2 Background ...... 161 A.3 Impurity Characterization ...... 163 A.4 Gas-mixing Facility Cleaning Methods ...... 170 A.5 Shock Tube Cleaning Methods ...... 173 A.6 Additional Comments ...... 177

B Microwave Discharge System 179 B.1 Introduction ...... 179 B.2 Equipment Setup and Procedure ...... 179 B.3 Results ...... 181 B.4 Conclusions ...... 183

C Fuel Measurement using a Helium-neon Laser 185 C.1 Introduction ...... 185 C.2 Equipment ...... 185 C.3 Mixing Time Determination ...... 186 C.4 Mole Fraction Measurements in a Multi-pass Cell ...... 187

D Rate Constant Estimation Methods 199 D.1 Introduction ...... 199 D.2 Empirical Estimation Methods ...... 201 D.3 Transition State Theory ...... 207 D.4 Ab initio Prediction Methods ...... 208

E Estimation of Rate Constants for Unimolecular Reactions 211 E.1 Introduction ...... 211 E.2 High-pressure Limit ...... 213

xiii E.3 Fall-oﬀ Limit ...... 215

Bibliography 217

xiv List of Tables

2.1 Double-dilution mixture preparation procedure example to prepare a mixture of 50 ppm TBHP/water and 150 ppm n-heptane in argon. . 21

3.1 Reactions added and rate constants modiﬁed in the JetSurf 1.0 mechanism to generate the alkane/TBHP mechanism used for this study. 31 3.2 Measured rate constant for Reaction (3.1) from 799 to 990 K. . . . . 39

4.1 Individual data points ﬁt using the alkane/TBHP mechanism for the

rate constant for Reaction (4.1): C5H12 + OH −→ C5H11 + H2O. . . 58 4.2 Individual data points ﬁt using the alkane/TBHP mechanism for the

rate constant for Reaction (4.2): C7H16 + OH −→ C7H15 + H2O. . . 58 4.3 Individual data points ﬁt using the alkane/TBHP mechanism for the

rate constant for Reaction (4.3): C9H20 + OH −→ C9H19 + H2O. . . 59

5.1 List of reactions and rate constants of the n-butanol/TBHP mechanism of the current work...... 79 5.2 Determinations of the rate constant for Reaction (5.1) from the experimental OH time-history data...... 83 5.3 Individual and coupled uncertainties and inﬂuence of the uncertainties on the determination of the rate constant for Reaction (5.1) at 1197 K and 925 K...... 89 5.4 Diﬀerences in the mechanisms in the current work and the work of Vasu et al...... 92

xv 6.1 Rate constants for the reactions of signiﬁcance in iso-butanol kinetics that were added to the base mechanism...... 102 non-β overall 6.2 Rate constants k6.1 and k6.1 for each experimental data point, and the resulting branching ratio for the β-channel...... 107

7.1 Rate constant determination for Reaction (7.1) for each experimental data point...... 123

8.1 Pseudo-ﬁrst-order and second-order rate constants determined for each experimental temperature...... 135 8.2 Rate constants determined for each experimental temperature. . . . 141

D.1 Group rate constants from Walker...... 203 D.2 Improved group scheme rate constant terms recommended by Sivara- makrishnan and Michael...... 207

E.1 Families of addition reactions with equivalent rate constants. . . . . 214

xvi List of Figures

1.1 Reaction path diagram for the n-heptane autoignition process showing many of the major reaction pathways...... 5 1.2 Average composition of commercial gasoline in the United States as reported in Pitz et al...... 7 1.3 The four structural isomers of butanol ...... 10

2.1 Position-time (x-t) diagram of a standard pressure driven shock tube operation and schematics of a shock tube at various times...... 15 2.2 Schematic of the cross-sectional view of shock tube...... 16 2.3 Schematic of the gas-mixing facility showing the diﬀerent elements connected to the 14-port gas-mixing manifold...... 18 2.4 Schematic of the laser diagnostic system...... 23

3.1 Two-step decomposition mechanism of tert-butylhydroperoxide. . . . 29 3.2 OH sensitivity for a mixture of 20.5 ppm TBHP in argon at 928 K and 1.22 atm...... 33 3.3 OH sensitivity for a mixture of 20.0 ppm TBHP in argon at 1158 K and 1.10 atm...... 33 3.4 OH time-histories at 928 K, 1.22 atm for 20.5 ppm TBHP argon. . . 35 3.5 OH time-histories at 1158 K, 1.10 atm for 20.0 ppm TBHP argon. . 36 3.6 Measured OH yield as a function of the initial TBHP/water solution mole fraction in a test mixture...... 38 3.7 Arrhenius plot of the rate constant for Reaction (3.1)...... 40

3.8 Arrhenius plot of rate constants for reactions of CH3 + OH...... 42

xvii 4.1 OH sensitivity for pseudo ﬁrst-order experiments to measure the overall rate of n-nonane+OH...... 53 4.2 OH time-histories at 1167 K, 1.00 atm for 168 ppm n-nonane, 16.0 ppm TBHP, argon...... 54 4.3 OH time-history on a semi-logarithmic scale for conditions of 937 K, 1.20 atm for 214 ppm n-nonane, 16.5 ppm TBHP, argon...... 56 4.4 Measured rate constants for Reactions (4.1), (4.2), and (4.3), reactions of OH with n-pentane, n-heptane, and n-nonane, respectively. . . . . 57 4.5 Factors considered in the uncertainty analysis for the rate constant for Reaction (4.3) at 1167 K, 1.00 atm...... 60 4.6 Rate constants for Reactions (4.1), (4.2), and (4.3)...... 63

5.1 OH time-histories from Chapter 3 for experiments of dilute mixtures of TBHP in argon...... 73 5.2 Arrhenius plot of the rate constant for Reaction (5.1)...... 74 5.3 Reaction pathways important in the calculation of OH time-history under the current experimental conditions...... 77 5.4 OH time-histories for 1197 K and 0.96 atm for a mixture of 150 ppm n-butanol and 13.3 ppm TBHP, and 925 K and 1.22 atm for a mixture of 201 ppm n-butanol and 10.3 ppm TBHP...... 82 5.5 OH sensitivity calculation for a mixture of 201 ppm n-butanol and 10.3 ppm TBHP at 925 K at 1.22 atm...... 84 5.6 OH reaction path analysis at 1197 K and 0.96 atm for a mixture of 150 ppm n-butanol and 13.3 ppm TBHP...... 86 5.7 Measured OH time-histories at 1182 K, 2.04 atm, 150 ppm n-butanol, 13 ppm TBHP and at 1165 K, 2.25 atm, 147 ppm n-butanol, 11 ppm TBHP...... 90 5.8 Arrhenius plot of the rate constant for Reaction (5.1)...... 92 5.9 Arrhenius plot of the rate constant for Reaction (5.1) shown with published data at atmospheric-relevant conditions...... 95

6.1 Dominant reaction pathways of iso-butanol after reaction with OH. . 98

xviii 6.2 OH sensitivity calculation at 1079 K, 1.1 atm with 220 ppm iso-butanol and 15 ppm TBHP...... 103 6.3 OH time-histories at temperatures of 1134 K, 1079 K, 1047 K, and 937 K...... 105 non-β 6.4 Rate constant measurements for k6.1 ...... 106 6.5 Overall rate constant for the reaction of OH with iso-butanol. . . . . 110

7.1 Dominant reaction pathways of sec-butanol after reaction with OH. . 115 7.2 OH sensitivity analysis of the 214 ppm sec-butanol and 14 ppm TBHP mixture at 969 K and 1.15 atm...... 117 7.3 Branching ratios for Reactions (7.1a) through (7.1e)...... 118

7.4 Branching ratios for the consumption of the CH2CH(OH)CH2CH3 and

CH3CH(OH)CHCH3 radicals...... 119 7.5 OH time-history for an experiment at 969 K, 1.15 atm with 214 ppm sec-butanol and 14 ppm TBHP...... 120 7.6 Arrhenius plot of the rate constant for Reaction (7.1)...... 121 7.7 Arrhenius plot of the rate constant for Reaction (7.1)...... 125

8.1 Dominant reaction pathways of tert-butanol after reaction with OH. 131 8.2 OH time-history at 943 K on a semi-logarithmic plot...... 134 8.3 Brute force sensitivity for the pseudo-ﬁrst-order rate constant. . . . . 137 8.4 OH reaction path diagram...... 138

8.5 Arrhenius plot of the product of k8.1 · (1 − brOH · brβ)...... 140 8.6 Arrhenius plot of the overall rate constant for Reaction (8.1). . . . . 141

8.7 The temperature-dependent branching ratio brβ...... 143 8.8 Arrhenius plot of experimental determinations for the overall rate constant for the reaction of OH with tert-butanol and the best-ﬁt 3- parameter expression...... 145

9.1 Arrhenius plot of the rate constant determinations for Reac- tions (5.1), (6.1), (7.1), and (8.1) from the current work...... 154

xix A.1 Schematic of the driven section of the Kinetics Shock Tube and gas- mixing facility...... 163 A.2 Impurity measurement history in the shock tube facilities...... 165

A.3 OH time-history measurements in hot 2% O2/Ar shocks near 1655 K for diﬀerent ﬁll locations in the shock tube...... 166

A.4 Peak OH mole fraction formed in hot 2% O2/Ar shocks around 1655 K as a function of ﬁll location...... 167

A.5 Peak OH mole fraction formed in hot 2% O2/Ar shocks at various temperatures and diﬀerent ﬁll locations...... 168

A.6 OH time-histories measured in 2% O2/Ar shocks, ﬁlled into the shock tube from the mixing facility...... 172

B.1 Schematic of He/H2O microwave discharge cell and H2O saturator setup...... 181 B.2 OH line shapes, calculated and measured...... 182 B.3 Measured OH line shape compared with the Doppler proﬁle ﬁt at a temperature of 800 K...... 183

C.1 Measured n-heptane mole fractions of a n-heptane/argon mixture after being filled into the shock tube after different mixing times...... 187 C.2 Alignment card setup for the multi-pass cell using the manufacturer supplied cards...... 189 C.3 Multi-pass cell setup with HeNe laser...... 189 C.4 Gas flow diagram of the multi-pass cell setup...... 192 C.5 Uncertainty in the measured mole fraction using an absorption diagnostic with a 3% uncertainty in laser intensity...... 193 C.6 Absorption measurements at various pressures of the 50 ppm TBHP/water in argon mixture...... 195

D.1 The carbons of the n-heptane and iso-butanol molecules described using the terminology used in this appendix...... 201

xx E.1 Three beta-scission decomposition pathways for the 1-hydroxy-but-2-yl radical...... 212

E.2 Isomerization reactions for C4H9O radicals...... 212

E.3 Rate constants for addition reactions of alkene+CH3 and alkene+OH from Manion et al...... 214

xxi xxii Chapter 1

Introduction

1.1 Motivation

Combustion has been a dominant process for energy conversion in automobiles since the development of the internal combustion engine in the 1800’s. Recent energy consumption statistics in 2011 from the United States Energy Information Agency point out that 94% of the energy used in our nation’s transportation sector comes from petroleum resources [1], indicating that combustion is still a dominant energy conversion process of importance. The continued use of petroleum-fueled automobiles in the present day introduces concerns revolving around future environmental impact, sustainability, and political and economic issues. In response to these concerns, research on the development of advanced transportation engine technologies capable of generating lower emissions, operating with increased eﬃciency, and/or converting energy from renewable resources, is being carried out in laboratories all over the world. Opti- mization of these advanced transportation engine technologies can be facilitated with accurate predictive models describing the combustion phenomena that occur within the engine. A predictive combustion model consists of mathematical descriptions of the transport, ﬂuid mechanics, and chemistry phenomena relevant to the combustion process. The development of these models typically begins with the development and validation of individual models for each phenomenon.

1 2 CHAPTER 1. INTRODUCTION

Chemical kinetics, the study of rates of chemical processes, is an important process to include in a comprehensive combustion model. Kinetic models are of critical importance in the design of certain types of advanced engine technologies. For example, the ignition event in a homogeneous charge compression ignition (HCCI) engine is controlled by the kinetics of combustion, as opposed to traditional spark-ignition or diesel engines where ignition is controlled by spark or injection, respectively. Rate constants for elementary reactions in the mechanism are a critical part of the model, and certain chemical species and reactions play key roles in the combustion process. Chemical species with unpaired electrons, called radicals, are important in every combustion process, and reactions of radicals with the combusting fuel can constitute a major fuel consumption pathway. Rate constants for these types of reactions must be known well to develop accurate detailed kinetic models for combustion. In this thesis, rate constants for important reactions in the combustion process were studied in a pressure-driven shock tube using laser-based diagnostics, and the results expand the experimental database of rate constants for use in the development of detailed kinetic mechanisms. The key reactions studied fall in the family of reactions of hydrogen-atom abstraction by the hydroxyl radical (OH) of a normal alkane molecule or an isomer of the butanol molecule; normal alkanes and butanol represent two families of organic molecules that are of current interest regarding transportation fuels. Narrow-linewidth laser absorption by OH was employed for quantitative time-resolved measurement of OH mole fraction in experiments designed with high sensitivity to the rate constants of interest. tert-Butylhydroperoxide (TBHP) was used as a fast source of OH radicals, and improvements to the modeling of the decomposition of TBHP as the OH precursor were also undertaken in this study.

1.2 Background

1.2.1 Development of Kinetic Mechanisms for Combustion

Accurate knowledge of the rate constants for the types of reactions studied in this thesis are of critical importance in developing accurate predictive kinetic mechanisms 1.2. BACKGROUND 3

for combustion. Detailed kinetic models for the high-temperature oxidation (combustion) of organic compounds contain three parts: 1) a list of each elementary reaction expected to occur in the process, 2) a rate constant for each elementary reaction, including a description of the rate constant dependence on temperature and pressure, and 3) thermodynamic parameters describing the temperature-dependent enthalpy and entropy for each chemical species present in the mechanism. A model with these three components constitutes a detailed kinetic mechanism. The number of elementary reactions needed to fully describe the combustion chemistry of a given fuel typically grows with the complexity of the fuel of interest. For example, a current detailed kinetic mechanism describing hydrogen combustion is comprised of 20 reactions with 10 chemical species [2]. A popular mechanism developed for methane combustion consists of 325 reactions and 53 chemical species [3], and a mechanism for n-heptane combustion has 2450 reactions and 550 chemical species [4]. Detailed kinetic mechanisms are often reduced to fewer reactions for computational simplicity; these reduced mechanisms, however, typically are limited in application and can be no more accurate than the detailed mechanism from which they originate. The rate constants for each of the elementary reactions in a mechanism are con- ventionally expressed in a modiﬁed Arrhenius form given by Eq. 1.1, where ki is the rate constant for Reaction (i) and its dependence on temperature, T , can be described using the three parameters A, b, and E.

! E k = A · T b · exp − (Eq. 1.1) i T

The parameters A, b, and E for each elementary reaction can be determined via several methods, including direct measurements, ab initio calculations, or estimations based on analogous reactions or global experimental studies. Because the number of reactions and rate constants needed in a detailed combustion kinetic model is large, many rate constants in a kinetic mechanism are typically determined using estimation techniques because of the time required for other methods of rate constant determination. However, several types of reactions are of high importance in predicting 4 CHAPTER 1. INTRODUCTION

experimental benchmarks, including the types of reactions in the current study, and the rate constants for these reactions must be ascribed accurately in a mechanism to correctly predict combustion behavior. Detailed kinetic mechanisms for combustion are often validated against a large number of experimental datasets. Shock tube ignition delay time experiments, measuring the time required for autoignition, are a common type of validation target for kinetic models. Similarly, multi-species time-history measurements in shock tubes during high-temperature pyrolysis and oxidation of fuels have recently gained popularity for validating kinetic models. Other experimental facilities such as flow reactors, rapid compression machines, jet-stirred reactors, and flames are also used by the experimental combustion community to expand the experimental database of validation targets for the development of detailed kinetic mechanisms. These types of experiments can elucidate deficiencies of kinetic mechanisms in development and suggest the need for refinement of the mechanism for increased accuracy. However, while these types of experiments provide valuable global validation targets, the data are typically sensitive to numerous rate constants in the mechanism, leading to difficulties in determining which rate constant are in error if the mechanism fails to predict the data. A reaction path diagram of a n-heptane autoignition process is shown in Figure 1.1, illustrating the number of reactions involved during this chemical process. Therefore, experiments designed specifically to be sensitive to important rate constants are crucial for improving kinetic model performance, in addition to the global validation targets. Shock tube reactors offer several advantages for high-temperature rate constant measurements, including a near-ideal constant volume test platform, well-determined temperatures and pressures behind the reflected shock waves, and clear optical access for laser diagnostics. Temperature, pressure, mixture composition, and measured data type are typical variables that can be varied in a shock tube experiment, and careful design of these variables can lead to experiments that isolate a reaction of interest. One such method to isolate a reaction in a shock tube study is to study a mixture of only the two reactants (typically in an inert diluent), and to monitor the time-dependent decay of one or several reactant or product concentrations. In the 1.2. BACKGROUND 5

Figure 1.1: Reaction path diagram for the n-heptane autoignition process showing many of the major reaction pathways. The percentages listed by the hydrogen-atom abstraction reactions represent the fraction of the reaction that occurs via abstraction with each speciﬁc molecule, calculated for a stoichiometric n-heptane/air mixture at 1000 K and 1 atm at a time of 20 ms using the Curran et al. mechanism [4]. study of bimolecular reactions, a pseudo-ﬁrst-order reaction approximation technique is commonly employed, where one reactant is present in large excess (over ten times) of the other reactant; this technique leads to an exponential decay of the concentration of the lower concentration reactant, and the time constant is typically sensitive to only the rate constant for the reaction and the initial concentration of the reactant in excess. As seen in Figure 1.1, the bimolecular reaction of OH with n-heptane is a major fuel consumption pathway under certain conditions, according to the kinetic mechanism of Curran et al. [4]. Thus, the rate constant for this reaction, and similar types of reactions, should be measured with high accuracy.

In the study of bimolecular reactions involving unstable radical species, such as the reactions of interest in this study, stable radical precursors that rapidly decompose via shock heating or laser photolysis can be used as a fast source for the radical reactant. Several stable species have been used as precursors for OH radicals, including hydrogen peroxide [5], tert-butylhydroperoxide [6–12], methanol [13], and 6 CHAPTER 1. INTRODUCTION

hydroxylamine [13], each having certain advantages and disadvantages. Challenges to experimental determination of rate constants arise when secondary reactions in- ﬂuence the measured data. These secondary reactions can include reactions due to secondary products of the decomposition of the stable radical precursor, or reactions of the products of the bimolecular reaction of interest. In this work, both of these issues appear, and the eﬀects are accounted for through experimental study and kinetic modeling.

1.2.2 Alkane Combustion Kinetics

Current commercial gasoline, diesel and jet fuels are composed of a mixture of organic compounds. Figure 1.2 presents the average composition of commercial gasoline in the United States as reported by Pitz et al. [14]. Alkane molecules, also known as paraf- ﬁns or saturated hydrocarbons or hydrocarbons with exclusively single bonds, are in the majority, making up over 50% of the gasoline composition. Many of these alkanes are large straight-chain normal alkanes (referred to as n-alkanes). In addition to their presence in current commercial fuels, n-alkanes are are also popular component choices for surrogate fuels, which are mixtures of a few select hydrocarbon compounds with combustion characteristics similar to those of commercial fuels. For example, n-heptane is widely used as a surrogate for gasoline, n-hexadecane a surrogate for diesel, and n-decane and n-dodecane as surrogates for jet fuel [14–16]. Furthermore, n-heptane is a primary reference fuel used to determine the octane rating of commercial gasoline. Because of the importance of large straight-chain n-alkanes in both practical and surrogate fuels, development of accurate kinetic mechanisms describing the combustion characteristics of n-alkanes is important. Kinetic mechanisms for hydrocarbon fuels, including n-alkanes, have been rapidly evolving over the past few decades. The ability to develop and run calculations with kinetic mechanisms for large n-alkane fuels has only recently been made possible, owing to the substantial improvements in computing systems, which are now capable of performing calculations for the thousands of reactions in these mechanisms in a reasonable time frame. Several long-term development projects for high-temperature 1.2. BACKGROUND 7

Alkanes Average Composition of Naphthenes Commercial U.S. Gasoline Olefins Aromatics 6.06% 9.6%

56.6%

27.8%

Figure 1.2: Average composition of commercial gasoline in the United States as reported in Pitz et al. [14]. Representative structures of each type of molecules are shown in the chart.

kinetic mechanisms of large n-alkane exist. For example, n-heptane combustion chemistry can be found in the mechanisms suggested by Curran et al. [4], Ranzi et al. [17], and Smith et al. [18], among others. The rapid progress in the development of larger kinetic mechanisms for larger fuels calls for expansion of the experimental database for validating these mechanisms at a similar rate. The current work contributes to expanding the experimental database for the kinetics of large n-alkanes, speciﬁcally rate constants for reactions of OH with n-pentane (C5H12), n-heptane (C7H16), and n-nonane (C9H20). To date, only estimation methods have been developed [11, 19–26] to predict the temperature dependence of the rate constant for the reaction of OH with n-nonane at combustion-relevant temperatures, and thus, the current work seeks to extend the experimental database of rate constants to validate these estimation methods. Using the data presented in this thesis, the accuracy of estimation methods to obtain rate constants for reactions in the family of OH plus n-alkanes will be examined to increase the conﬁdence in predicting the rate constants for this family of reactions involving even larger n-alkanes. 8 CHAPTER 1. INTRODUCTION

1.2.3 Butanol Combustion Kinetics

Factors such as unstable oil prices, a desire for increased sustainability and energy security, and concerns about greenhouse gas emissions from fossil fuels have led to increased efforts to introduce biofuels into the current transportation economy. Biofuels are fuels derived from biological carbon fixation, thus the combustion of biofuels leads to lower net carbon dioxide emissions as compared to gasoline (a common misconcep- tion is that biofuel combustion always leads to “net zero” carbon emissions; however, the processes used to produce and transport many biofuels typically lead to some carbon dioxide emission). Because biofuels can be produced from renewable organic material, with common feedstocks including animal fats, corn, and sugarcane, supply can ideally be infinitely renewable, and production of biofuels is not limited to only certain areas of the world. Furthermore, study of the combustion of oxygenated hydrocarbon fuels, such as bio-alcohol fuels, has shown that the presence of oxygenated compounds in the fuel mixture can suppress soot formation in diesel engines [27]. The most widely used liquid biofuel in the transportation sector currently is bio- derived ethanol, produced by fermentation of crops such as corn or sugarcane. In the United States, ethanol fuel is largely introduced into traditional vehicles in low- level blends with gasoline up to 10%. Commercially available flex-fuel vehicles have recently become increasingly popular, which have modified internal combustion engines that are capable of operating on a maximum blend of 85% ethanol with 15% gasoline (called E85 fuel). While use of ethanol as a transportation fuel has attributed to some success in increased energy security and reduced greenhouse gas emissions, there are still shortcomings to using ethanol fuel, including low energy density, properties incompatible with several components of current internal combustion engines (thus the need for modified flex-fuel engines for operation on E85 fuel), and difficulties in transporting ethanol in the current gasoline infrastructure because ethanol is miscible with water. Biobutanol is a second-generation biofuel for transportation applications and has many advantages over ethanol. Compared with ethanol, butanol has a higher energy density, a lower propensity to attract water (thus it can be more easily transported 1.2. BACKGROUND 9

and stored in the current gasoline infrastructure), and properties suitable for operation in unmodified gasoline engines [28]. Biobutanol can be produced via similar production methods as ethanol (via the acetone-butanol-ethanol process) using feedstocks such as corn and sugarcane. In addition, biobutanol can also be made from lignocellulosic sources like crop waste and non-food plants such as switch grass. Pro- duction of biobutanol from algae is also possible. The energy content of butanol still falls short of the energy content of gasoline, however, combustion of 100% butanol fuel will occur over a more uniform temperature and pressure compared to gasoline (the many components of gasoline leads to ignition over a broad range of temperature and pressure). Thus, engines optimized for operation on 100% butanol fuel can be tuned to deliver a high fuel economy. Butanol is a four-carbon alcohol and has four structural isomers: n-butanol, iso- butanol, sec-butanol, and tert-butanol; these structural isomers of butanol are shown in Figure 1.3. Methods for producing n-butanol, iso-butanol, and sec-butanol from biological sources are currently known. While no methods have been established for the production of tert-butanol from biological matter, this isomer of butanol is widely used as a fuel additive. Thus, all four isomers of butanol are relevant as transportation fuels and detailed kinetic mechanisms describing the high-temperature oxidation of each of the butanol isomers are important. Detailed chemical kinetic models for high-temperature combustion of the isomers of butanol have become of recent research interest, lending support to the introduction of biobutanol into the transportation sector. The efforts towards kinetic modeling of n-butanol combustion is by far the most extensive. Dagaut and coworkers [29, 30] published one of the first kinetic mechanisms of n-butanol in 2008, using data from a jet-stirred reactor as validation targets. In the same year, Moss et al. [31] collected shock tube ignition delay time data for all four of the isomers of butanol and developed a kinetic mechanism including high-temperature chemistry for each isomer. Researchers from around the world quickly followed suit, adding to the literature additional mechanisms and experimental validation targets for n-butanol and the other isomers. Mechanisms for butanol combustion continue to be improved upon in the current day, indicating that work in this area is far from complete and that a larger 10 CHAPTER 1. INTRODUCTION

n-butanol iso-butanol

CH3 H2 H2 C C CH OH H3C C OH H3C C H2 H2

sec-butanol tert-butanol

OH CH3

CH CH3 H3C C OH H3C C H2 CH3

Figure 1.3: The four structural isomers of butanol kinetic experimental database would be beneficial. Various experimental targets of global butanol combustion phenomena have been collected in different types of reactor systems, including jet-stirred reactor species profiles [29, 30, 32], rapid compression machine and shock tube ignition delay times and speciation studies [31, 33–39], and flame studies [32, 40–46]. However, relatively few experimental data exist describing phenomena with high-sensitivity to key elementary reactions. The first measurements for the high-temperature rate constant for the reaction of OH with n-butanol was performed by Vasu et al. [47] in 2010. Besides the study of Vasu et al., however, no other experimental studies published in the literature directly focus on the rate constant for the reactions of OH with butanol at combustion-relevant temperatures. The current work extends upon the work of Vasu et al., extending the temperature range of their measurements and producing the first experimentally determined high- temperature rate constants for the reaction of OH with the other butanol isomers.

1.3 Scope and Organization of Thesis

The objective of this thesis is to collect low-noise OH time-history measurements at experimental conditions designed to have high sensitivity to the rate constants for 1.3. SCOPE AND ORGANIZATION OF THESIS 11

the reactions of the OH radical with n-alkane and butanol molecules at combustion- relevant conditions. These data expand the experimental database for n-alkane and butanol combustion kinetics and can be used for the validation and reﬁnement of kinetic mechanisms for the respective fuels. Three large n-alkanes (n-pentane, n- heptane, and n-nonane) and the four isomers of butanol (n-butanol, iso-butanol, sec-butanol, and tert-butanol) were studied. In the process of completing this work, several other research areas were examined, including the development of a fuel mole- fraction measurement method for ultra-low concentration experiments, experimental study and modeling of tert-butylhydroperoxide as a stable precursor for OH radicals, and detailed modeling studies of butanol after reaction with OH. Chapter 2 of this thesis discusses the experimental facilities and methods used for the data collection, including a discussion of the precautions taken to minimize experimental error and a description of the method developed for validating fuel concentration in ultra-low concentration mixtures. Chapter 3 introduces tert- butylhydroperoxide (TBHP) as a stable source of OH radicals, and present the results of experiments designed to develop a model for high-temperature TBHP decomposition. Chapter 4 presents the results of the experimental work on n-pentane, n-heptane, and n-nonane, and also includes discussion of the comparison of the current data with previous experimental, theoretical, and empirical modeling studies. Chapters 5 through 8 present the experimental work for n-butanol, iso-butanol, sec-butanol, and tert-butanol, and also include discussions on butanol combustion modeling and comparison to previous works. Supporting work, including discussions on preparing the experimental facilities and background on rate constant estimation methods, are included in the Appendices. At the time of publication, the contents of this thesis appear in several publications. The contents of Chapters 3 and 4 are adapted with permission from G. A. Pang, R. K. Hanson, D. M. Golden, and C. T. Bowman, “High-temperature measurements of the rate constants for reactions of OH with a series of large normal alkanes: n-pentane, n-heptane, and n-nonane,” Zeitschrift f¨urPhysikalische Chemie, Volume 225, 2011, Pages 1157-1178; copyright c 2011 Oldenbourg Wissenschaftsverlag GmbH. The content in Chapter 5 is adapted with permission from G. A. Pang, R. K. Hanson, 12 CHAPTER 1. INTRODUCTION

D. M. Golden, and C. T. Bowman, “Rate Constant Measurements for the Overall Re- action of OH + 1-Butanol → Products from 900 K to 1200 K,” Journal of Physical Chemistry A, Volume 116, 2012, Pages 2475-2483; copyright c 2012 American Chem- ical Society. The content in Chapter 6 is adapted with permission from G. A. Pang, R. K. Hanson, D. M. Golden, and C. T. Bowman, “High-temperature Rate Constant Determination for the Reaction of OH with iso-Butanol,” Journal of Physical Chem- istry A, Volume 116, 2012, Pages 4720-4725; copyright c 2012 American Chemical Society. Chapter 2

Experimental Setup

2.1 Introduction

The first shock tube was constructed in France in 1899 [48], though this type of device was not applied to the study of high-temperature chemical kinetics until the 1950’s [49]. The advantages of using a shock tube for the experimental study of high- temperature kinetics include instantaneous heating by shock waves, well-determined initial temperatures and pressures behind reflected shock waves, near-ideal constant volume reaction reaction environment, and clear optical access for laser diagnostics. The use of laser diagnostics to probe high-temperature reacting experiments enables the collection of in situ, time-resolved, species-specific measurements. This chapter details the shock tube facility and diagnostics utilized for the experiments performed in this work, as well as the basic procedures that were followed.

2.2 Kinetics Shock Tube Facility

The experiments reported in this thesis were all performed behind reﬂected shock waves in the Kinetics Shock Tube Facility located in the Mechanical Engineering Research Laboratory (MERL) of Stanford University. This shock tube facility consists of a pressure-driven shock tube and a high-purity gas mixing system.

13 14 CHAPTER 2. EXPERIMENTAL SETUP

2.2.1 Shock Tube Overview

The Stanford Kinetics Shock Tube is a pressure-driven stainless-steel shock tube with a circular cross-section of 14.13 cm (inner-diameter) in both the 8.54-m long driven section and the 3.35-m long driver section. The low-pressure driven section is separated from the high-pressure driver section by a polycarbonate diaphragm of 0.127 to 0.254 mm in thickness (Polycarbonate film DE1-1 Gloss/Gloss supplied by Professional Plastics). In a typical experiment, a premixed gas-phase test mixture is first filled into the driven section. The driver section is then subsequently filled to high-pressure with helium, or a mixture of helium and nitrogen, until the diaphragm is ruptured by a set of cross-shaped cutting blades residing on the driven-section side of the diaphragm. The rupture of the diaphragm allows the high-pressure driver gas to expand, creating an incident shock wave that propagates towards the driven-section endwall before subsequently reflecting back towards the driver section. Behind the reflected shock wave near the driven-section endwall is a high-temperature reaction environment closely representing a constant volume reactor. The shock tube process can be best represented on a position-time (x-t) plot, which is shown in Figure 2.1 for the operation of a standard pressure driven shock tube. The temperature and pressure behind the reflected shock wave are controlled by changing the incident shock velocity. In the current work, this was achieved by changing the thickness of the diaphragm, changing the axial position of the cutting blades responsible for the diaphragm rupture, and/or changing the composition of nitrogen in the driver gas. Five axially-spaced piezoelectric pressure transducers (PCB model no. 113A26 with 483B08 amplifier) were positioned at 2.0 cm, 38.8 cm, 69.3 cm, 99.7 cm, and 130.2 cm from the driven-section endwall for measurement of the incident-shock velocity. The signals from these pressure transducers were sent to four time-interval counters to determine the average incident shock velocity at four axial positions near the driven-section endwall. The measured incident-shock attenuation, typically in the range of 0.5-1.5%/m, was used to extrapolate the incident-shock velocity at the driven-section endwall. The reflected-shock velocity was calculated from the endwall incident-shock velocity, assuming a zero-axial-velocity boundary condition at the endwall. 2.2. KINETICS SHOCK TUBE FACILITY 15

region representing constant volume reactor

t2 > t1, reflected shock pressure transducers

d (shock velocity te n ec io measurement) fl ct re fa re n e a fa c t > t , incident shock r a k 1 0 rf c u ho s s fan t t n c en sio ta id an n c p o in ex c

t path particle x

Driver Driven section t , before diaphragm burst section 0

diaphragm driven section endwall

Figure 2.1: Position-time (x-t) diagram of a standard pressure driven shock tube operation and schematics of a shock tube at various times. Also shown in one of the time schematics are axially- spaced pressure transducers that can be used to measure the shock velocity.

The pressure and temperature conditions behind the reflected shock waves were determined using adiabatic one-dimensional shock relations and the known (measured) incident-shock velocities. These calculation were performed using an in-house code that contained thermodynamic data for the gas mixture; the results are identical to calculations using thermodynamic data from Goos et al. [50] for the species present in the gas mixture. Vibrational equilibrium was assumed in the gases behind the incident and reflected shock waves. Uncertainty in the incident-shock velocity determination at the driven-section endwall leads to uncertainties of less than 1% in both the reflected-shock temperatures and pressures at the measurement location. The reactive gas mixture behind the reflected shock wave was monitored at an axial location 2 cm from the driven-section endwall using a Kistler piezoelectric pressure transducer (PZT, model no. 603B1 with 5010B amplifier) and the laser absorption diagnostic discussed in Section 2.3.1. The PZT was mounted such that its surface was recessed approximately 1 mm from the inner diameter surface and the surface was coated with a layer of red silicon RTV approximately 1 mm thick to protect the sensor 16 CHAPTER 2. EXPERIMENTAL SETUP

from thermal shock and temperature-induced changes in sensitivity. The signal from the PZT was used to conﬁrm uniform pressure during the experiments. The laser absorption diagnostic was used to monitor the test gas 2 cm from the driven-section endwall through a pair 0.75” diameter sapphire windows of 0.125” thickness mounted directly opposite of each other tangent and ﬂush to the inner surface of the shock tube. Figure 2.2 shows a schematic of the cross-sectional view of the shock tube at the axial location 2 cm from the driven-section endwall with the diagnostics used in this thesis.

Cross-sectional view of the shock tube diagnostic area located 2 cm from the driven section endwall

PCB 113A26

Kistler 603B1

0.75'' diameter sapphire UV laser windows, 0.125'' thickness

Figure 2.2: Schematic of the cross-sectional view of shock tube at the axial location 2 cm from the driven-section endwall. The pressure transducers and the windows for the laser absorption diagnostics are shown, along with the alignment of the laser through the windows. The laser beam is angled to avoid interference from internal reﬂections.

The shock tube facility was thoroughly cleaned before the start of experiments, and also between experiments as needed. Prior to each set of experiments, the impurities in the shock tube were conﬁrmed to contribute to less than 1 ppm of hydrogen atoms using the laser diagnostics described in Section 2.3.1. Further details of the shock tube cleaning procedures and impurity detection is described in Appendix A. Before each individual experiment, the shock tube driven section was evacuated to a pressure at or below 5×10−6 Torr using a combination of a roughing pump and a turbomolecular pump. This vacuum corresponded to a shock tube leak-plus-outgassing rate at or below 50 × 10−6 Torr/minute. An ion gage tube vacuum sensor was connected to the vacuum sections to measure the ultimate pressure of the shock tube. Experiments were performed with and without passivation of the shock tube walls 2.2. KINETICS SHOCK TUBE FACILITY 17

using the initial mixture, a technique that has previously been demonstrated to reduce losses of chemicals due to wall adsorption [51]. The results of the passivation experiments concluded that passivation has no eﬀect and is thus unnecessary. Mea- surements of the fuel mole fraction in the prepared gas mixtures using the laser absorption technique described in Appendix C further conﬁrm that no liquid fuel loss occurs.

2.2.2 Gas-mixing Facility Overview

The experimental test mixtures were all prepared in a gas-mixing facility consisting of a 12-liter internally-stirred electro-polished stainless-steel mixing tank and a 14- port gas-mixing manifold. The mixing tank contains a brass mixing vane coupled to a magnetic stirrer, controlled by a Fischer Scientific Thermix Stirrer (Model 220T); the stirrer controller was set to medium speed and never turned off. The mixing manifold is constructed with a central welded stainless steel piece of cross pipe of 3/8” diameter, and each port can be connected to various sources via Swagelok stainless steel 8BK bellow valves. Figure 2.3 shows a schematic of the gas-mixing facility and the ports used for the experiments described in this thesis. A 100 Torr and a 10,000 Torr high-capacitance Baratron manometer (both Model 690A) were each located at different mixing manifold ports. The gas-mixing facility is connected to the shock tube driven section at a location 5.74 m from the driven-section endwall via a port on the mixing manifold. The gas-mixing facility has a two-stage evacuation procedure, with separate roughing and turbomolecular pumps than the shock tube. The vacuum pumps were connected to the mixing facility through a mixing manifold port when used for evacuation of the manifold, and were also connected to the mixing tank through a larger diameter valve for evacuation of the mixing tank and entire facility. An ion gage tube vacuum sensor was connected to the vacuum line to measure the ultimate pressure of the mixing facility. The gas-mixing facility was thoroughly cleaned using a brute-force disassembly method prior to the start of the experiments in this thesis, and chemical cleaning methods were used between each set of experiments. The laser diagnostic system described in Section 2.3.1 was used to periodically verify 18 CHAPTER 2. EXPERIMENTAL SETUP

that less than 1 ppm of hydrogen atom impurities were present in the mixing facility. Appendix A describes the cleaning and impurity detection methods used in this work. 10000 Torr Baratron Argon empty empty empty empty

100 Torr vent to atmosphere Baratron to shock tube (5.74 m from the driven section endwall) to vacuum pumps empty

Mixing

liquid chemical #2 Tank liquid chemical #1 (TBHP) 12 L

Figure 2.3: Schematic of the gas-mixing facility showing the diﬀerent elements connected to the 14-port gas-mixing manifold.

Three ports on the mixing manifold were used for the chemicals in the mixture preparation for this thesis work (Section 2.4 details the specific chemicals used). A single port was connected to a high-pressure argon gas cylinder through a CGA-590 regulator. Liquid chemicals for the experiments were placed in glass vessels (Chemglass part no. AF-0092-01 with an AF-0070-0 adapter), interfaced with the stainless-steel ports of valves of the mixing manifold via 3/8” Swagelok Ultra-Torr vacuum fittings. All liquid chemicals were purified using a freeze-pump-thaw procedure; this procedure involves freezing the liquid chemical using a thermos filled with liquid nitrogen, and then pumping with a combination of the roughing and turbomolecular pumps desig- nated for the mixing facility. Each time a new liquid chemical was connected to the mixing facility, the freeze-pump-thaw procedure was employed to remove the initial air in the vessel and any trapped gas impurities. The freeze-pump-thaw procedure was repeated several times for each chemical to increase the chemical purity. In the 2.2. KINETICS SHOCK TUBE FACILITY 19

first freeze-pump-thaw cycle, the liquid was pumped to an ultimate pressure of less than or equal to 1 × 10−6 Torr; in subsequent freeze-pump-thaw cycles, a vacuum of less than or equal to 1 × 10−3 Torr was achieved. For pure chemicals, the second and subsequent purification cycles typically omitted the freeze and thaw steps, employing only direct pumping of the vapors above the liquid with a roughing pump (for liquid mixtures such as the tert-butylhydroperoxide/water solution, the freeze and thaw steps were never omitted to prevent distillation of the solution). After purification of the liquid chemicals, the liquid vapors were introduced directly into the mixing facility, driven into the mixing facility by the pressure difference between the mixing facility and the liquid vapor pressure. In several cases where the vapor pressure of the liquid was not high enough to cause the vapor to flow into the mixing facility at an acceptable rate, a thermos filled of lukewarm water (approximately 35 ◦C) was used to raise the temperature, and thus the vapor pressure, of the desired liquid chemical.

The test mixtures in this work contain parts-per-million (ppm) levels of tert- butylhydroperoxide and a fuel component, diluted in argon (for the experiments in Chapter 3, the fuel component was omitted). The mixtures were all prepared using a double-dilution process to allow for accurate pressure measurements in the manometric preparation of highly dilute mixtures. The chemicals were introduced into the mixing tank through the manifold one at a time, with the vapors from the liquid chemicals first, typically in the order of increasing vapor pressure. In the first dilution stage, the 100 Torr manometer was used to measure the total pressure of the system (from which the partial pressures of each component was determined) during the introduction of the vapors from the liquid chemicals into the mixing tank. The 10,000 Torr manometer was used for measurement of total pressure after filling with the argon diluent. The partial pressures for the initial dilution stage were chosen based on the lowest vapor pressure of the chemicals in the mixture. After complete mixing of the initial mixing step, the mixture was diluted by evacuating part of the initial mixture, and diluting with additional argon. Each dilution stage was allowed to mix in the internally-stirred mixing tank for 45 to 60 minutes to ensure homogeneity and consistency. The mixing time was determined by utilizing the laser diagnostic system described in Appendix C. Table 2.1 presents a sample procedure for a mixture of 20 CHAPTER 2. EXPERIMENTAL SETUP

50 ppm TBHP/water and 150 ppm n-heptane in argon, and includes the total pressure after adding each chemical addition and dilution step. Each prepared mixture yields 4 to 8 experiments, depending on the temperatures and pressures of study. This limitation is set by the maximum pressure allowable in the mixing tank. The mixing tank and manifold are both equipped with electrical heating elements. For the experiments described in this thesis, both the mixing tank and manifold were electrically heated to approximately 50 ◦C to prevent condensation of liquid chemicals onto the stainless-steel surfaces. During the mixture preparation process, the pressure of the liquid vapors introduced into the mixing tank was never raised above one half of the room-temperature saturated vapor pressure of the liquid to avoid the possibility of condensation on the mixing tank walls.

2.3 Laser Diagnostics

2.3.1 OH Mole-fraction Diagnostic

The main component of the laser diagnostic system for quantitative OH detection is a Spectra-Physics 380 ring-dye laser cavity with a temperature-tuned intra-cavity AD*A frequency-doubling crystal. This ring-dye cavity was pumped with a Rho- damine 6G dye solution that was excited using a continuous-wave (CW) Coherent Verdi 532 nm solid-state laser. A schematic of the laser system and all of the optical components is shown in Figure 2.4. The Rhodamine 6G dye solution was prepared with 0.33 g/L of Rhodamine 6G (from Exciton, also called Rhodamine 590) in an ethylene glycol solvent (spectrophotometric grade ≥ 99% from Sigma Aldrich). This concentration of dye was found to provide the maximum laser power by Herbon [52]. Each prepared dye solution was allowed to mix for over 24 hours before being circu- lated through the dye-cavity. The dye solution in the laser system was periodically replaced with a new solution when the output laser power decreased signiﬁcantly. This laser system produced a 25 to 30 mW visible laser beam around 613.4 nm, and a 1 to 2 mW ultra-violet (UV) laser beam that was tuned to the center of the

R1(5) absorption line in the OH A–X (0,0) band near 306.7 nm. The majority of 2.3. LASER DIAGNOSTICS 21

Table 2.1: Double-dilution mixture preparation procedure example to prepare a mixture of 50 ppm TBHP/water and 150 ppm n-heptane in argon.

Step Action Mixing tank Mixing tank contents total pressure (Torr) 1 Evacuate entire mixing facility < 5 × 10−6 2 Add ∼5 Torr of the TBHP/water 5.08 100% TBHP/water solution to mixing tank 3 Isolate mixing tank. Evacuate manifold 4 Add ∼15 Torr of n-heptane 20.04 25% TBHP/water, 75% n-heptane 5 Isolate mixing tank. Evacuate manifold 6 Add argon 1007 0.5% TBHP/water, 1.5% n-heptane, argon 7 Isolate mixing tank. Evacuate manifold 8 Mix ﬁrst dilution stage for 45 minutes 9 Evacuate mixing tank to ∼50 Torr 50.39 0.5% TBHP/water, 1.5% n-heptane, argon 10 Isolate mixing tank. Evacuate manifold 11 Add argon to mixing tank limit 5005 50 ppm TBHP/water, 150 ppm n-heptane, argon 12 Mix second dilution stage for 45 minutes 13 Final mixture 50 ppm TBHP/water, 150 ppm n-heptane, argon 22 CHAPTER 2. EXPERIMENTAL SETUP

the visible light was monitored by a Burleigh WA-1000 visible wavemeter. A portion of the visible light was split off into a scanning interferometer system to monitor the mode quality and ensure single-mode operation. The majority of the UV light was directed into the diagnostic windows of the shock tube, located 2 cm from the driven-section end wall. The beam path entering the shock tube was slightly angled in the cross-sectional plane of the shock tube to minimize the possibility of internal reflections exiting the shock tube (see Figure 2.2). Several focusing optics consisting of CaF2 spherical lenses were placed in the beam path to prevent beam divergence and to shape the resulting beam diameter entering and exiting the shock tube to approximately 1.5 mm. A portion of the UV light was also split off upstream of the shock tube using a UV-grade beam splitter so that common-mode rejection could be employed to reduce the effects of noise caused by fluctuations in laser intensity. Both the intensity of the UV light beam split off upstream of the shock tube, and the intensity of the transmitted laser light exiting the shock tube were monitored through Schott Glass UG11 filters with in-house-modified UV-enhanced Thorlabs PDA36A photo-diode detectors, each with a bandwidth of 758 kHz. These detectors collected data at a rate of 1000 kHz. To monitor the wavelength of the laser light, the visible laser beam was directed into a Burleigh WA-1000 visible wavemeter. The accuracy of the visible light wavelength measurement is 0.016 cm−1 with proper alignment of the wavemeter, resulting in knowledge of the UV light wavelength to within 0.032 cm−1. Because larger inac- curacies in the wavemeter reading are possible due to poor alignment of the device, the visible laser beam from the dye cavity was aligned to follow a co-linear path with the emitted tracer laser of the wavemeter for over 1 m; improper alignment of the wavemeter was found to lead to errors of 0.05 cm−1. Furthermore, a microwave discharge lamp system, discussed in Appendix B, was employed to verify the correct wavemeter reading at the peak of the R1(5) absorption line in the OH A–X (0,0) band. The current optical system allowed for time-resolved quantitative measurement of the OH mole fraction (called OH time-histories) calculated using the Beer-Lambert Law, given by Eq. 2.1, where T is the measured fractional UV transmission, I is the 2.3. LASER DIAGNOSTICS 23

intensity of the transmitted UV beam, I0 is the intensity of the upstream split-off UV beam normalized by the initial fractional transmission, kν is the absorption coefficient for OH, L is the path length equal to the shock tube diameter, P is the reflected-shock pressure, and x is the measured mole fraction of OH.

I T = = exp(−kν · P · x · L) (Eq. 2.1) I0

The absorption coeﬃcient for OH was taken from work of Herbon [52] who provided temperature- and pressure-dependent values accounting for broadening of the lineshape.

Burleigh wavemeter

Coherent Verdi pump laser Scanning interferometer

f = 100 cm 532 nm Spectra-Physics ring-dye cavity Detector

306.7 nm 613.4 nm (UV) (visible) f = 10 cm Legend

Flat plate beam splitter UV-grade beam splitter Shock tube Mirror UG11 filter

CaF2 spherical lens f = 6 cm Iris Modified PDA36A detector

Figure 2.4: Schematic of the laser diagnostic system used in this work to generate ultra-violet laser light near 306.7 nm for OH absorption in the A–X (0,0) band. Image adapted from Herbon [52].

The time zero in the measurement trace was defined as the instant of the reflected shock passing at the measurement location. The time zero could be inferred from the measured data trace at the appearance of a Schlieren effect, caused because the laser beam is momentarily steered off the detector by the large density gradient at the shock 24 CHAPTER 2. EXPERIMENTAL SETUP

wave, and is visually manifested as a 3-µs-wide spike in the transmitted signal; the time zero was deﬁned as the peak of this spike. The noise in the measured fractional UV transmission was less than 0.1% before time zero; however, beam steering occurs after the passing of the shock waves at the measurement location, therefore, after time zero the measured fractional UV-transmission noise was typically ±0.4% or less. Under typical experimental conditions the minimum OH mole fraction detectivity is approximately 1.5 ppm. The experiments in this work were designed such that the signal-to-noise ratio at the peak OH mole fraction is greater than or equal to six. All sets of experiments in this thesis were examined for two main types of diagnostic interference. Oﬀ-line absorption measurements with the UV laser wavelength

tuned off of the R1(5) absorption line were performed for all different test mixtures used, and these measurements did not reveal any interference (background) absorption. Measurements of each different test mixture with the UV laser blocked were also performed, and the results verified that the transmitted signals do not include any molecular emission. In addition to collecting time-resolved OH mole fraction time-histories during experiments, this OH absorption diagnostic technique was also used to periodically verify the cleanliness of the combined shock tube, mixing tank, and mixing manifold system as described in Appendix A.

2.3.2 Organic Fuel Mole Fraction Diagnostic

An infra-red Jodon Helium-Neon laser (HeNe, Model HN-10GIR) of wavelength 3.39 µm was utilized to determine the mixing time required for the mixture preparation process, and also to verify the composition of the double-dilution-prepared mixtures of n-heptane and n-butanol. Light absorption at a wavelength of 3.39 µm occurs due to the C–H stretch mode, and thus, the mole fraction of any absorbing species can be determined using Eq. 2.1 if the absorption cross-section for each chemical of interest at 3.39 µm is known. An absorption cross-section for n-heptane from Klingbeil et al. [53] was used in determining the n-heptane mole fraction, and an absorption cross-section for n-butanol was taken from Sharpe et al. [54]. The 2.3. LASER DIAGNOSTICS 25

intensity of the HeNe laser light was measured using liquid-nitrogen-cooled indium antimonide (InSb) detectors from IR Associates (model no. IS-2.0). The procedure for determining the mixing time required for the mixture preparation process is described in Appendix C along with the procedure for verifying the composition of the double-dilution-prepared mixtures. A brief description of the latter procedure will be provided here.

An experimental setup containing the 3.39 µm HeNe laser system and an external multi-pass absorption cell (Toptica Photonics model no. CMP30) of total path length 30 m was designed to confirm the composition of the experimental test mixture. This confirmation is necessary to eliminate concerns about the possibility of wall adsorption occurring in the experimental facility, and the long-path-length external multi-pass cell is needed for adequate absorption to occur due to the highly-dilute mixtures of interest in this work. The composition of the double-dilution-prepared mixture was verified for several n-heptane and n-butanol mixtures by sampling a portion of the final mixture prepared, using the process described in Section 2.2.2, into the external multi-pass absorption cell. The total pressure of the gas mixture in the cell was chosen such that the absorption of the HeNe laser light passing through the cell was between 10% and 90% (in all cases, several pressures were examined to test the repeatability of the mole fraction measurements). Mixtures of n-heptane (or n-butanol) in argon, TBHP in argon, and n-heptane (or n-butanol) and TBHP in argon were examined. The mixtures of TBHP in argon were used to determined the absorption cross section of the TBHP/water solution (see Section 2.4 for chemical description) to ∼2 m2 per mole of TBHP/water solution (because the amount of TBHP/water solution in the mixtures of interest is relatively small compared to the amount of fuel, this absorption cross-section did not require measurement to high accuracy). The mixtures with n-heptane or n-butanol were first introduced into the cell initially through the mixing manifold, and it was confirmed that no fuel loss occurred during the mixing process. The mixtures were also introduced into the cell through a port at 2 cm from the driven-section endwall (so the mixture would be filled into the shock tube from the mixing tank before entering the multi-pass cell, simulating an actual experiment), and the mixture composition in the shock 26 CHAPTER 2. EXPERIMENTAL SETUP

tube was conﬁrmed to be equivalent to what was expected from the manometric preparation, with a measurement uncertainty of the fuel concentration of ±5%. The other n-alkanes and isomers of butanol studied in this thesis have similar properties to n-heptane and n-butanol, respectively, and therefore no fuel loss will be assumed for all mixtures prepared in this thesis and this measurement uncertainty is taken to be the overall uncertainty of the fuel concentration in all mixtures prepared. More details of the multi-pass cell setup, alignment procedures, and measurement results are discussed in Appendix C.

2.4 Test Mixture Chemicals

A commercially available solution of 70%, by weight, tert-butylhydroperoxide (TBHP) in water, from Sigma Aldrich (Luperox TBH70X, product no. 458139), was used in all experiments described in this thesis. The TBHP/water solution was stored chilled at -8 ◦C until typically the day of its introduction into the mixing tank (in a few instances, the solution had up to three days of residence at room temperature). Argon gas (99.998% purity), supplied by Praxair, Inc., was used as the mixture diluent for all experiments in this work. Additional chemicals that were used particular to speciﬁc chapters in this thesis will be described in their respective chapters. Chapter 3

Decomposition of tert-Butylhydroperoxide

3.1 Introduction

3.1.1 Background

In the high-temperature study of reaction kinetics involving one or more highly- reactive radical species, stable chemical species are typically used as precursors to generate the radical(s) of interest. For example, kinetic studies involving the hydroxyl (OH) radical have employed several diﬀerent stable chemical precursors, including hydrogen peroxide [5], tert-butylhydroperoxide [6, 8–12], methanol [13], and hydroxylamine [13]. Methods applying laser photolysis techniques also allow for OH radicals to be generated through photolysis and reaction of a combination of chemicals, such as H2O with N2O [55] and N2O with NH3 [56]. Each of these methods of generating OH radicals has certain advantages and disadvantages that vary depending on the conditions of interest.

The use of tert-butylhydroperoxide (TBHP: (CH3)3COOH) as an OH precursor was pioneered by Cohen and coworkers [6–9] in the 1980’s, when they used the stable compound for the study of rate constants for reactions of OH with various organic compounds in shock tubes at temperatures near 1100 K. One advantage of TBHP

27 28 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE

as an OH precursor is its ease of handling as compared with hydrogen peroxide, the latter of which is corrosive on stainless-steel reactor surfaces. A second advantage is that TBHP undergoes rapid decomposition at temperatures as low as 1000 K (with a characteristic decomposition time of ∼1 µs at 1000 K). Many recent eﬀorts in advanced engine technologies utilized intermediate- or low-temperature combustion at temperatures around 1000 K or lower, and thus kinetic experiments are needed near these temperatures for model validation. Thus, other stable chemical species that are commonly used as OH precursors, such as methanol and hydroxylamine (each with characteristic decomposition times >100 µs at 1500 K), are limited in use for experiments in this temperature range.

A current drawback to using TBHP as an OH precursor is the secondary reaction chemistry due to the additional chemical species formed during TBHP decomposition. TBHP generates OH radicals and other products during its two-step decomposition mechanism described by Reactions (3.1) and (3.2).

(CH3)3COOH −→ (CH3)3CO + OH (3.1)

(CH3)3CO −→ CH3 + CH3COCH3 (3.2)

Figure 3.1 illustrates this two-step decomposition mechanism. In addition to OH radicals, methyl radicals and acetone molecules are also formed, and these molecules can be involved in secondary elementary reactions during the experiment that aﬀect the OH radical pool, such as Reactions (3.3) and (3.4).

CH3 + OH −→ CH2(s) + H2O (3.3)

CH3COCH3 + OH −→ CH2COCH3 + H2O (3.4)

In Reaction (3.3), CH2(s) represents the excited singlet state of CH2. Using a detailed mechanism to accurately account for relevant secondary reactions that occur during TBHP decomposition can address the changes in the OH radical pool due to TBHP- related secondary chemistry.

Another drawback of TBHP as an OH precursor for combustion-relevant 3.1. INTRODUCTION 29

CH CH 3 OH 3 H3C O H3C C O + OH

CH3 CH3

H3C C O + CH3

H3C

Figure 3.1: Two-step decomposition mechanism of tert-butylhydroperoxide into ﬁnal products of OH, methyl, and acetone via Reactions (3.1) and (3.2). Red arrows illustrate movement of electrons that occur during the reactions. intermediate-temperature experiments is that TBHP has limited use as a simple OH precursor at temperatures lower than 1000 K. Because most combustion reactions occur on time scales on the order of tens to hundreds of µs, at temperatures lower than 1000 K where the OH formation from TBHP decomposition takes several µs to occur, the rate of decomposition, governed by the rate constant for Reaction (3.1), inﬂuences the observations of the reactions of interest. While measurements of the rate constant for Reaction (3.1) have been presented in the literature by several sources [57–62], large scatter in these data exist and improvements to the accuracy of those measurements can contribute to improved understanding of low-temperature experiments employing TBHP as an OH precursor.

3.1.2 Objectives of the Current Chapter

In this chapter, the results of experiments designed to be sensitive to the rate constants for elementary reactions important in TBHP decomposition are presented. OH time-histories were measured in experiments of TBHP, dilute in argon, in the temperature range from 799 to 1316 K, and a detailed kinetic mechanism was created to accurately describe the background chemistry occurring during and after TBHP 30 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE

decomposition.

3.2 TBHP Kinetic Mechanism

3.2.1 Mechanism Generation

A chemical kinetic mechanism detailing TBHP chemistry, and also including alkane chemistry for use the subsequent chapter, was generated to model the eﬀect of TBHP kinetics on measured OH time-histories. The base of this mechanism is the JetSurF 1.0 mechanism [18], with Reactions (3.1), (3.2), (3.5a) and (3.5b) added for TBHP chemistry.

(CH3)3COOH + OH −→ (CH3)3C + H2O + O2 (3.5a)

−→ (CH3)2C−CH2 + H2O + HO2 (3.5b)

All reactions were considered to be reversible.1 Thermodynamic parameters for TBHP and tert-butoxyl were obtained from the thermodynamic database from Goos et al. [50], and the thermodynamic parameters for OH were updated from Herbon et al. [52]. The rate constant for Reaction (3.1) was set to the rate measured by Vasudevan et al. [61] for initial analysis, however, this rate constant was updated to that which was measured in Section 3.5 of this work for the final analyses of this chapter, and subsequent chapters of this thesis. The rate constant for Reaction (3.2) was taken from Choo and Benson [63], the rate constant for Reaction (3.5a) was estimated to be half the rate constant for the reaction OH + H2O2 −→ HO2 + H2O as measured by Hong et al. [64], and the rate constant for Reaction (3.5b) was estimated to be half the rate constant for the reaction OH + tetramethylbutane −→ Products as measured by Sivaramakrishnan and Michael [11]. The rate constant for Reaction (3.3) was modified to fit the TBHP chemistry as determined in Section 3.5. Updated rate constants were used for Reaction (3.4) for acetone chemistry from Vasudevan et al. [12] and for

1The reversibility of reactions is considered for all reactions written in this thesis, even though an arrow in only the forward direction is always used 3.2. TBHP KINETIC MECHANISM 31

Reactions (3.6) and (3.7) for hydrogen/oxygen chemistry from Hong et al. [2].

H + O2 −→ OH + O (3.6)

OH + OH −→ H2O + O (3.7)

The reactions added to the JetSurF 1.0 mechanism and the updated rate constants are listed in Table 3.1. From this point forward, the detailed mechanism compiled as described above will be referred to as the alkane/TBHP mechanism. Some repre- sentation of this alkane/TBHP mechanism will be used for the analysis of all of the experiments described in the subsequent chapters of this thesis.

Table 3.1: Reactions added and rate constants modiﬁed in the JetSurf 1.0 mechanism to generate the alkane/TBHP mechanism used for this study. Units for A are [cm3molecule−1s−1] for bimolecular reactions and [s−1] for unimolecular reactions, units for E are [cal mol−1K−1].

No. Reaction k = A · T b exp(−E/RT ) Reference A b E

+13 4 (3.1) (CH3)3COOH −−→ (CH3)3CO + OH 3.57 × 10 0.0 +3.57 × 10 This work +14 4 (3.2) (CH3)3CO −−→ CH3 + CH3COCH3 1.26 × 10 0.0 +1.53 × 10 [63] −11 (3.3) CH3 + OH −−→ CH2(s) + H2O 2.74 × 10 0.0 0.00 This work −11 3 (3.4) CH3COCH3 + OH −−→ CH2COCH3 + H2O 4.90 × 10 0.0 +4.59 × 10 [12] −11 3 (3.5a) (CH3)3COOH + OH −−→ (CH3)3C + H2O + O2 3.82 × 10 0.0 +5.22 × 10 [64] −11 3 (3.5b) (CH3)3COOH + OH −−→ (CH3)2C−CH2 + H2O + 4.13 × 10 0.0 +2.66 × 10 [11] HO2 −10 4 (3.6) H + O2 −−→ OH + O 1.73 × 10 0.0 +1.53 × 10 [2] −20 3 (3.7) OH + OH −−→ H2O + O 5.93 × 10 2.4 −2.11 × 10 [2]

The CHEMKIN-PRO R suite of programs by Reaction Design was used to perform analyses with this alkane/TBHP mechanism in this chapter and all subsequent chapters of this thesis. Constant volume and constant internal energy constraints were placed on all simulations.

3.2.2 OH Sensitivity Analysis

Figures 3.2 and 3.3 show the top four reactions appearing in the results of OH sensitivity analyses at 928 K and 1158 K, respectively, using the alkane/TBHP mechanism for mixtures of approximately 20 ppm TBHP dilute in argon. The OH sensitivity is 32 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE

deﬁned by Eq. 3.1 where SOH,i is the time-dependent OH sensitivity to the rate con-

stant for Reaction (i), xOH is the local time OH mole fraction, and ki is the rate constant for Reaction (i).

∂xOH ki SOH,i = · (Eq. 3.1) ∂ki xOH

The OH sensitivity describes the influence of a perturbation on ki on the simulated OH time-history. The results of the OH sensitivity analyses indicate that Reaction (3.3) (the reaction of OH with methyl radicals) is important in defining the simulated OH time- history under both temperatures examined. Other reactions involving methyl radicals, acetone, and OH radicals, all final products of the TBHP decomposition, are also important to varying degrees, depending on the simulation conditions. The rate constant for Reaction (3.1) appears as a dominant reaction in the OH sensitivity analysis for temperatures below 1000 K. The rate constant for Reaction (3.7) was updated with the recommendation from Hong et al. [2], whose review of this reaction reveals that measurements from various studies converge to an agreed-upon rate constant. The rate constant for Reaction (3.4) has been measured by Vasudevan et al. [12] with a 25% uncertainty, and is the rate constant used in this analysis. Therefore, the rate constants for these two reactions are considered adequately accurate for the analyses in this thesis work. Accurate knowledge of the rate constants for Reactions (3.1) and (3.3) is not as readily available in the literature, and thus the current chapter discusses the results of experiments designed to determine these rate constants as necessary for future experiments using TBHP as an OH precursor in shock tube experiments.

3.3 Experimental

The experiments in this chapter were conducted with the experimental setup and chemicals described in Chapter 2. OH time-histories were measured after the shock- heating of dilute mixtures of the TBHP solution in argon. While the actual mixture 3.3. EXPERIMENTAL 33

1.0 (3.1) (CH ) COOH -> (CH ) CO + OH 3 3 3 3 (3.3) CH + OH -> CH (s) + H O 0.8 3 2 2 CH +OH(+M) -> CH OH(+M) 3 3 0.6 CH +CH (+M) -> C H (+M) 3 3 2 6

0.4 (3.1)

0.2

OH Sensitivity 0.0

(3.3) -0.2 928 K, 1.22 atm 20.5 ppm TBHP, argon -0.4 0 102030405060 Time [s]

Figure 3.2: OH sensitivity for a mixture of 20.5 ppm TBHP in argon at 928 K and 1.22 atm illustrating the importance of the rate constant for Reaction (3.1) in the early-time (<30 µs in this case) simulated OH time-history under these conditions. The simulated OH time-history is most sensitive to the rate constant for the reaction shown with a solid line, Reaction (3.1), and the rate constant for this reaction can be determined from a measured OH time-history under these conditions.

0.1 1158 K, 1.10 atm 20 ppm TBHP, argon

0.0 (3.1) (3.4) (3.7)

-0.1 (3.3)

OH Sensitivity (3.1) (CH ) COOH -> (CH ) CO + OH -0.2 3 3 3 3 (3.3) CH + OH -> CH (s) + H O 3 2 2 (3.4) CH COCH + OH -> CH COCH + H O 3 3 2 3 2 (3.7) OH + OH -> H O + O -0.3 2 0 20406080100 Time [s]

Figure 3.3: OH sensitivity for a mixture of 20.0 ppm TBHP in argon at 1158 K and 1.10 atm illustrating the importance of the rate constant for Reaction (3.3) in the simulated OH time-history under these conditions. The simulated OH time-history is most sensitive to the rate constant for the reaction shown with a solid line, Reaction (3.3), and and the rate constant for this reaction can be determined from a measured OH time-history under these conditions. 34 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE

has a small fraction of water, the presence of water is not expected to have an eﬀect on the measurement; thus, the mixtures will be referred to as TBHP only in this chapter, and the subsequent chapters. Several test mixtures were prepared for the experiments discussed in this chapter; the composition of the mixtures ranged from 20 to 30 ppm of TBHP diluted in argon. The reﬂected-shock conditions were controlled to generate temperatures in the range of 799 to 1316 K under pressures of 1 to 3 atm. For the dilute mixtures and short test times in the current experiments, the measured reaction pressure (and thus temperature) remains constant. The measured OH time-histories were analyzed with the kinetic mechanism described in Section 3.2 with constant volume and constant internal energy constraints.

3.4 OH Mole Fraction Measurements

3.4.1 OH Time-history

Sample measured OH time-histories for mixtures of approximately 20 ppm TBHP in argon are shown in Figures 3.4 and 3.5 for reflected-shock conditions of 928 K and 1.22 atm, and 1158 K and 1.10 atm, respectively. Simulated OH time-histories are also shown, and these are discussed in Section 3.5. As evident from the measured OH time-histories shown in Figures 3.4 and 3.5, the decomposition of TBHP upon heating in a shock tube does not lead to a step-function source of OH radicals (which is the ideal case for a radical precursor). Thus, a model describing the OH time- history behavior due to TBHP decomposition is needed to accurately analyze any experiments monitoring the OH mole fraction in mixtures containing TBHP, and this can be done by using accurate rate constants for key reactions in the alkane/TBHP mechanism described in Section 3.2. Note that a main difference between the two measured traces in Figures 3.4 and 3.5 is the finite time (greater than 1 µs) required for the formation of OH at 928 K versus the near instantaneous formation of OH from the decomposition of TBHP to OH at 1158 K. All measured OH time-histories at temperatures below 1000 K demonstrate slow decomposition trends similar to as shown in Figure 3.4; the rate of OH formation 3.4. OH MOLE FRACTION MEASUREMENTS 35

at these temperatures is used to determined the rate constant for Reaction (3.1), and the results are presented in Section 3.5. Similarly, all measured OH time-histories at temperatures above 1000 K show near-instantaneous OH formation like in Fig- ure 3.5, with a subsequent OH decay following the peak OH mole fraction. The rate of the measured subsequent OH decay is used to determine the rate constant for Reaction (3.3), and the results are also presented in Section 3.5.

20 928 K, 1.22 atm 20.5 ppm TBHP, argon 16

8 Data

1.0 x k3.1 0.7 x k

OH mole fraction [ppm] 4 3.1

1.3 x k3.1 Reaction (3.1): (CH ) COOH -> (CH ) CO + OH 3 3 3 3 0 0 102030405060 Time [μs]

Figure 3.4: Measured OH time-histories at 928 K, 1.22 atm for 20.5 ppm TBHP argon. Also shown are simulated OH time-histories with the best-ﬁt rate constant for Reaction (3.1) and perturbations of ±30% on the best-ﬁt rate constant.

3.4.2 OH Yield

The commercial TBHP/water solution described in Chapter 3 that the test mixtures were prepared from is 70% by weight TBHP, which equates to about 30% by mole liquid concentration of TBHP in water. However, because this is a non-ideal solution, the concentration of TBHP in the vapor phase is not simple to calculate. At temperatures above 1000 K, all of the initial TBHP decomposes almost instantaneously into OH radicals and other products, as shown in Figure 3.5, thereby allowing inference of the initial TBHP concentration (assumed to be equal to the peak concentration 36 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE

1158 K, 1.10 atm 20 20 ppm TBHP, argon

Data 8 1.0 x k 3.3 0.7 x k 3.3 OH mole fraction [ppm] 4 1.3 x k 3.3 Reaction (3.3): CH + OH -> CH (s) + H O 3 2 2 0 0 20406080100 Time [μs]

Figure 3.5: Measured OH time-histories at 1158 K, 1.10 atm for 20.0 ppm TBHP argon. Also shown are simulated OH time-histories with the best-fit rate constant for Reaction (3.3) and perturbations of ±30% on the best-fit rate constant. of OH formed) directly from each high-temperature (>1000 K) measured OH time- history. For each given mixture, the measured value of initial TBHP composition was typically consistent within 10% from shock to shock. In a few mixtures, if the mixing tank was heated to higher than 50 ◦C (e.g. if the controller to the electrical heating element was not setting the temperature correctly), the initial TBHP composition would noticeably drop from shock to shock, possibly indicating that some initial decomposition of TBHP was occurring inside the shock tube; these effects were examined and found to negligibly influence the rate constant determinations in the subsequent chapters. The OH yield can be determined in experiments at temperatures above 1000 K, and is defined as the measured peak OH mole fraction divided by the initial mole fraction of the TBHP/water solution Figure 3.6 presents the measured peak OH mole fraction for a representative set of experiments at temperatures above 1000 K as a function of the initial mole fraction of the TBHP/water solution. The initial mole fraction of the TBHP/water solution 3.4. OH MOLE FRACTION MEASUREMENTS 37

is determined from manometric preparation, which is described in Chapter 2. At temperatures above 1000 K, all of the measured OH can be assumed to be instantaneously formed from TBHP in a one-to-one ratio; therefore, in these experiments, the TBHP yield from the TBHP/water solution can be defined as the measured peak OH mole fraction divided by the initial mole fraction of the TBHP/water solution. The total amount of TBHP yield from the TBHP/water solution was found to be between 20 and 32% across all the mixtures prepared (in the experiments in this chapter and the subsequent chapters). The measured TBHP yields are similar to the TBHP yields found by other researchers who performed similar experiments [47, 62, 65, 66], with the exception of Vasudevan [67] who consistently found a lower TBHP yield, which could possibly be attributed to adsorption or decomposition in the mixing tank or premature TBHP decomposition prior to introduction in the mixing facility. The TBHP yields discovered in the current work indicate that the solution vapor composition is similar to the liquid solution composition. The deviations of TBHP yield from mixture to mixture could be due to different residence times of the TBHP/water solution outside of the chilled storage, where the TBHP may slowly decompose at room temperature, the result of a different pattern of pumping cycles during purification where the solution may consequently become partially distilled, or premature decomposition in the mixing tank due to excessive heating by the electric heaters. Adsorption of TBHP onto the stainless steel surfaces of the facility are also possible, as noted in other works [12, 62]. Uncertainties in the initial TBHP concentration, including effects of TBHP adsorption and premature decomposition, are addressed in the uncertainty analysis of the rate constant determinations in the subsequent chapters, and do not have a significant effect on the measured rate constants described in this thesis. In the simulated OH time-histories in this chapter (and subsequent chapters), the initial TBHP composition was inferred directly from the measured OH time- history as described above. For experiments at temperatures less than 1000 K, the initial TBHP composition could not be inferred directly due to the finite time require for the TBHP decomposition. Therefore, for low-temperature (<1000 K) experiments, an initial TBHP composition value in agreement with an inferred initial 38 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE

OH yield from TBHP/water solution 50 Current work ld ie Masten Y ld H ie Y Vasudevan O H 40 % O 2 Vasu et al. 3 0% Cook et al. 2 30

10 Measured peak OH yield [ppm] 0 0 50 100 150 200 Initial TBHP/water solution vapor [ppm]

Figure 3.6: Measured OH yield as a function of the initial TBHP/water solution mole fraction in a test mixture. Shown for the representative experimental work for this thesis, and also compared to other experiments in the literature [47, 62, 65–67]. Both data from mixtures of TBHP in argon (this chapter) and mixtures of TBHP and an organic compound (from subsequent chapters) in argon are included.

high-temperature-experiment TBHP composition from the same mixture was used in the kinetic simulations. In all kinetic simulations, an initial water concentration was prescribed in the mixture as the diﬀerence between the initial amount of TBHP measured and the amount of TBHP/water solution vapor originally placed in the mixture (known from the manometric preparation procedure); however, calculations have shown that the presence of water has a negligible eﬀect on the results, thus the prescription of water in the simulated mixture could be omitted if desired.

3.5 Rate Constant Determinations

3.5.1 Determination of k3.1

For the current experimental mixtures studied at temperatures below 1000 K, the simulated OH time-histories using the alkane/TBHP mechanism are highly sensitive to the rate constant for Reaction (3.1) at early times, as can be seen from the OH 3.5. RATE CONSTANT DETERMINATIONS 39

sensitivity analysis in Figure 3.2. The results of the measured OH time-histories from the experiments conducted at temperatures from 799 to 990 K and pressures from 1 to 3 atm were used to determine the rate constant for Reaction (3.1). The early-time simulated OH time-history was matched to the measured trace by changing only the rate constant for Reaction (3.1). Figure 3.4 shows a sample measured OH time-history and the early-time eﬀect of the rate constant for Reaction (3.1) on the simulated OH time-history. The rate constant for Reaction (3.1) as a function of temperature was determined from all of the experimental data traces at temperatures from 799 to 990 K, and the results are shown in Figure 3.7. The individual data points are also presented in Ta- ble 3.2. The data were taken at pressures from 1 to 3 atm, and no signiﬁcant pressure dependence was observed from the experimental data. Therefore, the measurements of the rate constant for Reaction (3.1) can be expressed in Arrhenius form by Eq. 3.2.

! 18000 k = 3.57 × 10+13 exp − s−1 (Eq. 3.2) 3.1 T [K]

Eq. 3.2 is valid for temperatures from 799 to 990 K and pressures from 1 to 3 atm.

Table 3.2: Measured rate constant for Reaction (3.1) from 799 to 990 K, determined from ﬁtting measured OH time-histories of TBHP dilute in argon with the alkane/TBHP mechanism, using the rate constant for Reaction (3.1) as the free parameter.

−1 T [K] P [atm] k3.1 [s ] 990 2.15 3.53 ×105 928 1.22 1.30 ×105 920 2.38 1.32 ×105 881 1.29 5.20 ×104 871 2.40 5.10 ×104 856 1.35 2.80 ×104 820 1.36 9.50 ×103 812 2.41 8.00 ×103 799 2.52 5.00 ×103 40 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE

Reaction (3.1): (CH ) COOH -> (CH ) CO + OH 3 3 3 3 1000 K 714 K 556 K 455 K 107 1000 K 909 K 833 K 769 K 5 6 10 10

3 5 10 10

] 1 4 -1 10 10

[s Current data: 1 to 3 atm -1 3 3.1 Arrhenius fit to current data 10 10

k Vasu et al. (2010): 0.5 to 3 atm 1.0 1.1 1.2 1.3 -3 Vasudevan et al. (2005): 2 to 3 atm 10 Vasudevan et al. fit (2005) Sahetchian et al. (1992): 1 atm -5 10 Mulder and Louw (1984): 1 atm Benson and Spokes (1968): high-pressure limit 10-7 Kirk and Knox (1960): 10-20 Torr 1.0 1.2 1.4 1.6 1.8 2.0 2.2 1000/T [K-1]

Figure 3.7: Arrhenius plot of the rate constant for Reaction (3.1) from the literature [57–62] and compared with the rate found in the current work.

The measured rate constant for Reaction (3.1) is compared to other works [57– 62] in Figure 3.7. While the rate constant for Reaction (3.1) has been measured by Vasudevan et al. [61] and Vasu et al. [62] using similar methods in approximately the same temperature range of interest, only one experimental data point in both of those studies was obtained in the absence of another organic compound in the experimental mixture. The current measurements focus on the kinetics of TBHP only, and therefore, uncertainties in the rate constants for reactions of other other organic compounds with the TBHP decomposition products are not of concern in the current analysis. An uncertainty analysis on this rate constant determination reveals that the major uncertainty contribution is the initial concentration of TBHP, which leads to an estimated ±30% uncertainty in this rate constant. The current determination for the rate constant for Reaction (3.1) agrees with most other measurements in the literature within combined uncertainty estimates. A discrepancy just outside of the combined uncertainty estimates exists near 1000 K with the rate constant determination from 3.5. RATE CONSTANT DETERMINATIONS 41

Vasudevan et al. [61]; though at temperatures near 1000 K where the discrepancy in this rate constant exists, the rate constant for Reaction (3.1) has minimal eﬀects on the overall rate constant determinations presented in the subsequent chapters of this thesis. Therefore, uncertainties in the rate constant for Reaction (3.1) at the temperature where this discrepancy exists will not inﬂuence the rate constant determinations in the subsequent chapters of this thesis. The rate constant given in Eq. 3.2 will be used in analysis of all data discussed in this thesis.

3.5.2 Determination of k3.3

Methyl radicals (CH3) are a byproduct of the decomposition of TBHP, and therefore, the rate constant for the reaction of OH with CH3 is important to consider in the analysis of OH time-history measurements in shock tube experiments using TBHP. At temperatures above 800 K, the rate constant for the overall reaction of

CH3 + OH −→ Products has been studied experimentally by Bott and Cohen [8], Krasnoperov and Michael [68], Srinivasan et al. [69], and Vasudevan et al. [51]. A theoretical study of the rate constant for reaction of CH3 + OH has also been performed by Jasper et al. [70] and Ree et al. [71]. Figure 3.8 shows that a factor of six discrepancy exists among the rate constants for the reaction CH3 + OH in the literature. To address the large discrepancy in the rate constant for Reaction (3.3) in the literature, the results of measured OH time-histories in the high-temperature decomposition of TBHP for temperatures from 799 to 1316 K were used for accurate determination of the rate constant.

The reaction channel of CH3 +OH yielding the speciﬁc products in Reaction (3.3) was claimed to be the major product channel at high temperatures [68, 69]; however, a recent study by Ree et al. presents calculations that show the reaction channel leading to the product CH3OH may also be signiﬁcant, though the rate constant for Reaction (3.3) is still the fastest. Therefore, even if accounting for other reactions channels for the reaction of CH3 + OH, a large discrepancy still exists in the rate constant for Reaction (3.3). The simulated OH time-history using the alkane/TBHP mechanism shows high 42 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE

] 1428 K 1111 K 909 K 769 K

-1 10

s Reaction (3.3): 1 -1 CH3 + OH -> CH2(s) + H2O Srinivasan et al. (2007) JetSurF 1.0 Mechanism (2009)1 Ree et al. (2011)1 Current work (799-1316 K)1 molecule 3 (k ) CH + OH -> Products 3.3 3

cm Bott and Cohen (1991) 1

-11 Krasnoperov and Michael (2004) Jasper et al. (2007): 760 Torr1 α

[10 Vasudevan et al. (2008) Vasudevan et al. (2008) μ 1 1 + OH Ree et al. (2011) 3 CH α k 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Azomethane precursor μ 1000/T [K-1] Methyl iodide precursor

Figure 3.8: Arrhenius plot of rate constants for reactions of CH3 + OH from the literature [8, 18, 51, 68–71] and compared with the rate constant for Reaction (3.3) from the current work.

sensitivity to the rate constant for Reaction (3.3) at all temperatures in mixtures of dilute TBHP in argon, as illustrated in Figures 3.2 and 3.3. Therefore, the rate constant for Reaction (3.3) can be determined by ﬁtting simulated OH time-histories to the measured traces by adjusting only the rate constant for Reaction (3.3), within the limits of the rate constants provided in literature, in the alkane/TBHP mechanism. Using the rate constant described by Eq. 3.3 in the alkane/TBHP mechanism was found to generate simulated OH time-histories that best ﬁt the experimental data over the entire temperature range studied (799 to 1316 K).

−11 3 −1 −1 k3.3 = 2.74 × 10 cm molecule s (Eq. 3.3)

The best-ﬁt simulated OH time-history using the alkane/TBHP mechanism with this rate constant for Reaction (Eq. 3.3) is shown in Figure 3.5, along with the simulated OH time-histories with the rate constant perturbed by ±30%. The uncertainty in this rate constant determination for Reaction (3.3) is primarily due to ﬁtting the 3.5. RATE CONSTANT DETERMINATIONS 43

data trace, thus the expected the overall uncertainty of this rate constant is approximately ±30%. The uncertainty of the rate constants for secondary reactions can also contribute to the uncertainty in the rate constant determination for Reaction (3.3); however, because uncertainties in these secondary rate constants are not well known, it is difficult to determine the effects on the current rate constant determination. The work here proposes a rate constant for Reaction (3.3) that correctly predicts OH time-histories in experiments with TBHP, given the current secondary chemistry used; further comments on this uncertainty is discussed at the end of this section. Comparison of the current rate constant determination for Reaction (3.3) is shown in Figure 3.8. The current rate constant determination is 34% slower than the original rate constant from the JetSurf 1.0 mechanism. The experiments in the work of Vasudevan et al. [51] utilized two different stable precursors for methyl radicals (azomethane and methyl iodide), each paired with TBHP as the OH precursor. Their experiments show high sensitivity to the rate constant for Reaction (3.3) and span the temperature range 1081 to 1426 K. The current rate constant determination suggested by Eq. 3.3 agrees well with the measurements from Vasudevan et al., and therefore the current determination rate constant for Reaction (3.3) is assumed to be accurate up to temperatures of 1426 K. The current rate constant determination shows reasonable agreement with the experimental results of Bott and Cohen [8] and Krasnoperov and Michael [68], and also with the theoretical calculations of Jasper et al. [70] and Ree et al. [71]. Discrepancies exist between the current rate constant determination and the rate constant from Srinivasan et al. [69]; however, the results in the work of Srinivasan et al. were determined from experiments of dilute methanol decomposition, and their rate constant determination was found to be sensitive to other secondary rate constants and also show discrepancies with an earlier study from the same authors [69]. The recent study by Ree et al. [71] on the rate constants associated with all reaction channels of CH3 + OH claims that the pressure-dependent reaction channel leading to the products CH3OH should be considered. Figure 3.8 shows the rate constant for the overall reaction of CH3 + OH −→ Products predicted by Ree et al. is approximately twice the rate constant for Reaction (3.3). In the alkane/TBHP 44 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE

mechanism, the rate constant for the reaction CH3 + OH −→ CH3OH is from the JetSurF 1.0 mechanism [18], and this rate constant does become signiﬁcant relative to the rate constant for Reaction (3.3) at temperatures less than 1000 K, agreeing with the branching ratio predictions of Ree et al. [71]. According to the rate constants in the alkane/TBHP mechanism, the branching ratio of the overall reaction of CH3 +OH that proceeds via Reaction (3.3) is 55% at 800 K, though at temperatures above 1000 K, this branching ratio is greater than 70%. Thus, the rate constant for the reaction CH3 + OH −→ CH3OH becomes important at low temperatures, as shown by the OH sensitivity analysis in Figure 3.2. While there may be uncertainty in the current determination of the rate constant for Reaction (3.3) due to uncertainty in the branching ratio, using the currently suggested rate constant in the alkane/TBHP mechanism yields a detailed kinetic mechanism that is expected to correctly simulate the OH time-history in shock tube experiments with TBHP for temperatures from 799 to 1426 K. Thus, any rate constant errors cancel out, and this mechanism can be used for accurate analysis in any shock tube experiments of mixtures containing TBHP in this temperature range.

3.6 Summary

The rate constant measurements obtained in this section for TBHP chemistry are used in the alkane/TBHP mechanism compiled in Section 3.2, and the resulting mechanism correctly predicts the OH decay rate resulting from TBHP chemistry from approximately 800 to 1400 K. Table 3.1 lists all of the reactions and rate constants which were added and modiﬁed in the JetSurf 1.0 [18] base mechanism to create the alkane/TBHP mechanism in this work. The majority of the subsequent work presented in this thesis uses this alkane/TBHP mechanism either as the sole mechanism for analysis or as the base for which further reactions are added to include kinetic descriptions for additional species (i.e. butanol). The exception is in Chapter 7 where an alternate approach was used, involving the creation of a mechanism capable of accurately describing the 3.6. SUMMARY 45

TBHP-related OH time-histories by using the reactions and rate constants in Ta- ble 3.1 in other published mechanisms, instead of using the JetSurf 1.0 mechanism as a starting point. This alternate approach is also discussed in some detail in Chap- ter 5, and is expected to be successful in converting the majority of published kinetic mechanisms to accurately simulate TBHP-related kinetics. Simple calculations to verify that converted mechanisms simulate OH time-histories that match the measured traces in Figures 3.4 and 3.5 should always be done to conﬁrm the accuracy of any mechanism created with reactions and rate constants in Table 3.1 for TBHP chemistry. 46 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE Chapter 4

Reactions of OH with n-Alkanes

4.1 Introduction

4.1.1 Background

As mentioned in Chapter 1, the rate constants for reactions of OH with n-alkanes are important in the kinetic mechanisms describing the combustion of many current practical and surrogate fuels. Many experiments have been performed to measure the rate constants for n-alkane+OH at low-temperatures (250 to 440 K) [72–82], and recent studies have extended the experimental database with high-temperature (800 to 1300 K) data for several n-alkanes [6, 7, 9–11]. Attempts to measure the rate constants for reactions of OH with large n-alkanes become increasingly diﬃcult with increasing molecular weight of the alkane because the alkane vapor pressure typically decreases with increasing molecular weight. This results in diﬃculties introducing high concentrations of the alkane into the experimental apparatus in the gas phase (preparation of gas-phase mixtures is typically preferred for kinetic experiments because of the ease of creating a homogeneous mixture). Therefore, diagnostics capable of measuring highly dilute mole fractions of OH, such as the diagnostics described in Chapter 2, are necessary for experiments with large n-alkanes. Most detailed kinetic mechanisms involving large alkanes use estimated rate constants [18, 83, 84], usually obtained through an additivity scheme, with parameters

47 48 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

based on experimental data of measured rate constants for smaller alkanes. For example, a simple estimation method could assume a fixed rate constant for OH reacting with hydrogen atoms at each primary carbon site, and a different rate constant at each secondary carbon site. Greiner [19] was the first to develop an estimation method which resembles this approach for reactions of OH with n-alkanes. Recent literature has reported new rate constant estimation methods developed for reactions of OH with n-alkanes yielding improved agreement with experimental data [11, 20, 22, 25, 82]. Confidence in the accuracy of all of the estimation methods used for generating rate constants for reactions reactions of OH with n-alkanes is limited by the experimental database. For reactions of OH with n-alkanes, the availability of experimental data for rate constants above 800 K decreases with increasing length of the n-alkane chain. For example, the largest n-alkane studied in the works of Cohen and coworkers [6, 7, 9] was n-decane with a single-temperature-point measurement around 1100 K, while Michael and coworkers [10, 11] made measurements of the temperature dependence of the reactions of n-alkane+OH for temperatures from 800 to 1300 K for a series of alkanes, where n-heptane was the largest n-alkane studied. Therefore, there is a need to extend the experimental database of rate constants for reactions of OH with n-alkanes to larger normal alkanes, and to improve knowledge of the temperature dependence of these rate constants.

4.1.2 Objectives of the Current Chapter

The work in this chapter determines the rate constants for the overall reactions of

OH with three large normal alkanes: n-pentane (C5), n-heptane (C7) and n-nonane

(C9).

C5H12 + OH −→ C5H11 + H2O (4.1)

C7H14 + OH −→ C7H13 + H2O (4.2)

C9H20 + OH −→ C9H19 + H2O (4.3)

High-temperature shock tube experiments employing laser absorption by OH at 4.2. EXPERIMENTAL 49

306.7 nm were used to measure the OH time-history behind reﬂected shock waves under experimental conditions that are kinetically pseudo-ﬁrst-order in OH. The OH radicals were generated by the near-instantaneous decomposition of tert- butylhydroperoxide (TBHP), which generates an OH radical and a tert-butoxyl radical that subsequently decomposes into a methyl radical and acetone. Measurements of the rate constants for Reaction (4.1), (4.2), and (4.3) are compared with several estimation methods in the literature that predict the rate constant for reactions in the family of hydrogen-atom abstraction by OH of n-alkanes.

4.2 Experimental

The shock tube and laser diagnostics described in Chapter 2 of this thesis were used for the experimental work described in this chapter. In addition to the chemicals described in Chapter 2 (TBHP/water solution 70%, by weight TBHP, and argon gas), spectrophotometric grade n-pentane and n-heptane (each ≥ 99%), and anhydrous n-nonane (≥ 99%), all from Sigma Aldrich, were used in the mixture preparation. Mixtures of tert-butylhydroperoxide (TBHP) with an n-alkane in excess and diluted in argon were prepared; the mixture compositions of the experiments in this chapter are listed in Tables 4.1, 4.2 and 4.3. Reﬂected-shock pressures between 0.74 and 2.1 atm were used, and all mixture compositions had an initial n-alkane-to-TBHP concentration ratio greater than or equal to ten to yield near-pseudo-ﬁrst-order kinetics in OH. Measurements of OH time-histories at various temperature and pressure conditions represent the data collected.

4.3 Data Analysis

The measured OH time-histories presented in this chapter were analyzed using a pseudo-ﬁrst-order technique and also using a detailed kinetic model to infer the rate constants for Reaction (4.1), (4.2), and (4.3). Each technique is discussed in the subsequent subsections, and the advantages and disadvantages of each method are also described. A comparison of the ﬁnal rate constant results using the two analysis 50 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

methods is discussed in Section 4.4.

4.3.1 Pseudo-ﬁrst-order

A first-order reaction is a chemical reaction where the rate of reaction is proportional to the concentration of only one reactant. For a bimolecular reaction, the rate of the reaction typically depends on the concentration of both reactants. If, however, one reactant in a bimolecular reaction is present in large excess of the other reactant, a pseudo-first-order reaction is observed, as the concentration of the reactant in excess remains relatively constant. Thus, the rate law can be written as a function of the concentration of only one reactant, and resembles a first-order reaction rate law. For example, for Reaction (4.3), the rate law for the disappearance of OH can be written as Eq. 4.1, where the brackets around a chemical species refer to the time-dependent concentration of that species in the mixture.

d[OH] = −k [OH][C H ] (Eq. 4.1) dt 4.3 9 20

For the mixtures used in the experiments in this chapter, with n-nonane in excess of 0 OH, the rate law can be expressed in the pseudo-ﬁrst-order form of Eq. 4.2, where k4.3 is deﬁned by Eq. 4.3 and can be assumed constant, and the subscript t = 0 denotes the initial concentration.

d[OH] = −k0 [OH] (Eq. 4.2) dt 4.3 0 k4.3 = k4.3 · [C9H20]t=0 (Eq. 4.3)

The integrated form of the rate law in Eq. 4.2 results in Eq. 4.4, which expresses the 0 concentration of OH as a function of k4.3 and time only.

0 [OH] = [OH]t=0 exp(−k4.3 · t) (Eq. 4.4)

0 Thus k4.3 can be determined from the measurement of the exponential decay rate of the OH concentration, which can be determined from the measured OH time-history 4.3. DATA ANALYSIS 51

because the OH mole fraction is proportional to the concentration. The rate constant for Reaction (4.3) can be determined if the initial concentration of n-nonane is known, assuming that the approximations required for a pseudo-ﬁrst-order analysis are valid. An advantage of designing experiments where the concentration of the measured species follows a pseudo-ﬁrst-order (exponential) decay is that the rate constant determination is insensitive to the initial concentration of the chemical species measured

(i.e. [OH]t=0) and to the absolute value of the absorption coefficient for this species. For the experiments of the current chapter, this can be advantageous because small fluctuations in the initial concentration of OH occur, due to reasons specified in Sec- tion 3.4.2. Another advantage of the pseudo-first-order method is that the analysis is relatively simple and thus can be performed quickly. A major assumption required in applying the pseudo-first-order method to the work in this chapter is that secondary reactions have negligible influence on the measured OH time-histories. Systematic errors in the rate constant determination may arise if this assumption does not hold true.

4.3.2 Kinetic Modeling

Complete kinetic modeling of the experiments can account for any secondary reactions that might influence the simulated OH time-history. In addition to the pseudo-first- order method, the detailed alkane/TBHP mechanism developed in Chapter 3 was also used to determine the rate constants for Reaction (4.1), (4.2), and (4.3) from measured OH time-histories. The alkane/TBHP mechanism contains the JetSurF 1.0 mechanism [18], and therefore it already contains reactions relevant to n-alkane chemistry, and the modifications to the mechanism discussed in Chapter 3 account for the secondary chemistry from using TBHP as the OH precursor. The results of an OH sensitivity analysis performed with the alkane/TBHP mechanism under conditions of pseudo-first-order kinetics in OH are shown in Figure 4.1 for representative experiments with n-nonane at 1167 and 937 K. OH sensitivity is defined by Eq. 3.1, and the sensitivity to the overall rate constant for Reaction (4.3) 52 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

is defined as the sum of the OH sensitivity from all possible product channels. Fig- ure 4.1 illustrates that under these conditions at both temperatures, the simulated OH time-history is highly sensitive to the overall rate constant for Reaction (4.3). Reaction (3.3) also appears in the OH sensitivity results because this reaction also contributes to OH removal at both temperatures. Methyl radicals are generated from the decomposition of TBHP, and thus will be present at similar levels as OH. While increasing the alkane concentration could minimize the relative contribution of OH removal through this channel, this would also decrease the time scale of the experiment, which would also be undesirable. Therefore, if Reaction (3.3) contributes significantly to OH removal relative to Reaction (4.3), a detailed mechanism that correctly cap- tures the OH removal by Reaction (3.3), such as the alkane/TBHP mechanism from Chapter 3, is necessary in determining the rate constants for Reaction (4.3) and the other n-alkane+OH reactions. Another important reaction that must be accounted for when using TBHP as an OH precursor is Reaction (3.1), which is only significant in the OH sensitivity analysis shown in Figure 4.1 at 937 K (and also for any temperature below 1000 K). The rate constant for Reaction (3.1) was measured in Chapter 3. Because the rate constants of the significant secondary reactions appearing in the OH sensitivity analysis are well known, for a given experimental temperature, the rate constant for Reaction (4.3) can be determined by matching the simulated OH time-history with the measured data trace, using only the overall rate constant for Reaction (4.3) as a free parameter. While Reaction (4.3) can proceed via five different product channels, the identity of the products of Reaction (4.3) are assumed to have negligible influence on the rate constant determination, and this assumption was confirmed in a detailed uncertainty analysis that is presented Section 4.4. The results of OH sensitivity analyses for experiments with n-pentane and n- heptane are similar to those shown in Figure 4.1. Therefore, a method identical to the rate constant determination method for Reaction (4.3) is used to determine the rate constants for Reactions (4.1) and (4.2) from measured OH time-histories. A major advantage of using a detailed kinetic mechanism for the rate constant determination is that influences of secondary reactions are accounted for in the analysis. Because the 4.3. DATA ANALYSIS 53

alkane/TBHP mechanism developed in Chapter 3 was validated against experiments with neat TBHP dilute in argon, the mechanism is assumed to correctly describe the TBHP-related secondary chemistry, including Reactions (3.1) and (3.3). Therefore, if the rate constant results from the kinetic modeling method differ from that which was determined using the pseudo-first-order method, the rate constant determined using the kinetic modeling method is considered to be more representative of the actual rate constant. Because using a kinetic mechanism for the rate constant determination is more complex than the pseudo-first-order method, in certain cases the additional complexity and time required for the kinetic simulations may be unnecessary for experiments with negligible secondary chemistry; however, Section 4.4 shows that this was not found to be the case in the current experiments.

2 1167 K, 1.00 atm, 168 ppm C H , 16 ppm TBHP, argon 9 20 937 K, 1.20 atm, 214 ppm C H , 16.5 ppm TBHP, argon 9 20

-2 OH Sensitivity -4 / (3.1) (CH ) COOH -> (CH ) CO + OH 3 3 3 3 / (3.3) CH + OH -> CH (s) + H O 3 2 2 / (4.3) C H + OH -> C H + H O -6 9 20 9 19 2 0 20406080 Time [s]

Figure 4.1: OH sensitivity for pseudo ﬁrst-order experiments to measure the overall rate of n- nonane+OH, Reaction (4.3). Calculations with conditions for a representative high-temperature experiment (1167 K, 1.00 atm for 168 ppm n-nonane, 16.0 ppm TBHP, argon) are shown in black and has minimal secondary chemistry from Reaction (3.3). Calculations with conditions for a representative low-temperature experiment (937 K, 1.20 atm for 214 ppm n-nonane, 16.5 ppm TBHP, argon) are shown in red and illustrate larger OH sensitivity to TBHP decomposition, Reaction (3.1), at early times in addition to secondary chemistry from from Reaction (3.3). At both conditions, the simulated OH time-history is predominately sensitive to the rate constant for Reaction (4.3). 54 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

4.4 Results

4.4.1 Rate Constant Measurements

Figures 4.2 and 4.3 show sample measured OH time-histories for experiments with n- nonane at 1167 and 937 K, respectively. The OH time-histories follow an exponential decay, as expected from a pseudo-ﬁrst-order experiment; the exponential decay can

be seen more clearly on a plot of ln xOH versus time, as shown in Figure 4.2, or an semi-logarithmic plot of the OH time-history, as shown in the inset of Figure 4.3, where a linear decay is visible.

-2 -1 μ 1167 K, 1.00 atm 20 ) 2 Slope = -7.16x10 s 2 168 ppm C9H20, 1 [ppm] 16.0 ppm TBHP, argon OH

15 x ( 0 Current data 1 ln Linear fit -1 10 Simulations: -11 -2 k = 6.48 x 10 0 20406080 4.3 Time [μs] cm3molecule-1s-1 5 1 k -30%1

OH mole fraction [ppm] 4.3

k4.3 +30% 0 Reaction (4.3):

C9H20 + OH -> Products 0 20406080

Time [μs]

Figure 4.2: Measured OH time-histories at 1167 K, 1.00 atm for 168 ppm n-nonane, 16.0 ppm TBHP, argon. OH mole fraction trace is shown versus time (main plot), and the natural logarithm of the OH mole fraction is shown versus time (upper right). Also shown is a linear fit to ln xOH versus time and the simulated OH time-histories using the alkane/TBHP mechanism with the best-fit rate constant for Reaction (4.3) and perturbations of ±30% on the best-fit rate constant.

The time-constant of exponential decay (determined from the slope of ln xOH versus time) is the pseudo-first-order rate constant, defined by Eq. 4.3. For the experiment at the 1167 K shown in Figure 4.2, the pseudo-first-order rate constant 0 4 −1 is k4.3 = 7.16 × 10 s ; the concentration of n-nonane for the conditions in the 4.4. RESULTS 55

15 3 experiment is [C9H20] = 1.06 × 10 molecule/cm , leading to a rate constant for −11 3 −1 −1 Reaction (4.3) of k4.3 = 6.77 × 10 cm molecule s at 1167 K. The best-fit simulated OH time-history for the experimental conditions of Figure 4.2 is obtained using a rate constant for Reaction (4.3) of 6.48 × 10−11 cm3molecule−1s−1 in the alkane/TBHP mechanism. This simulated OH time-history is shown in Figure 4.2, along with perturbations of ±30% to k4.3. The pseudo-first-order method leads to rate constant determinations which are approximately 4% too fast at the current experimental conditions, primarily due to Reaction (3.3) (the reaction of OH with methyl radicals). In experiments with temperatures higher than 1000 K, the discrepancy between the rate constant determined from the pseudo-first-order method and the kinetic modeling method varies with the initial n-alkane-to-TBHP ratio and the identity of the n-alkane, reaching a discrepancy as high as 10% for experiments with initial n-pentane-to-TBHP ratios of ten. The rate constants determined using the kinetic modeling method are independent from the initial n-alkane-to-TBHP, supporting the assumption that the TBHP-related secondary chemistry is accounted for correctly. The discrepancy between the rate constant determined from the two analysis methods becomes larger than 10% at temperatures less than 1000 K for all n-alkanes studied, because the rate constant for Reaction (3.1) (the decomposition of TBHP) also influences the rate of OH decay. For these reasons, the kinetic modeling method is concluded to be a better method for inferring the most accurate rate constant from the current data for reactions of OH with n-alkanes.

While the time-constant describing the exponential decay of OH cannot be used directly to infer the rate constant for Reaction (4.3) without a systematic error due to neglecting the importance of Reaction (3.3), the exponential decay relationship is especially helpful in determining the rate constant that best ﬁts the OH time-history at temperatures below 1000 K, where the peak OH mole-fraction depends on the best-ﬁt rate constant for Reaction (4.3). For example, Figure 4.3 presents the OH time-history on a semi-logarithmic plot where the sensitivity of the peak OH mole- fraction to the rate constant for Reaction (4.3) is less prominent, and only the rate of OH decay is clearly seen to be sensitive to perturbations in the rate constant for Reaction (4.3). 56 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

937 K, 1.20 atm, 214 ppm C H , 16.5 ppm TBHP, argon 9 20

Reaction (4.3): C9H20 + OH -> Products Current data 1 10 -11 k4.3 = 4.65 x 10 cm3molecule-1s-1 1 k -30% 4.3 1

k4.3 +30%

1 OH mole fraction [ppm]

0.1 0 20406080 Time [μs]

Figure 4.3: Measured OH time-history on a semi-logarithmic scale for conditions of 937 K, 1.20 atm for 214 ppm n-nonane, 16.5 ppm TBHP, argon. Also shown are simulated OH time-histories using the alkane/TBHP mechanism with the best-ﬁt rate constant for Reaction (4.3) and perturbations of ±30% on the best-ﬁt rate constant.

The measured OH time-histories for the experiments in this chapter are all similar to the traces shown in Figures 4.2 and 4.3. Therefore, the kinetic modeling method can be applied to all OH time-history measurements of this chapter. The current determinations for the rate constants for the Reactions (4.1), (4.2), and (4.3) can be expressed in Arrhenius form by Eq. 4.5, Eq. 4.6, and Eq. 4.7, respectively.

! 2038 k = 2.10 × 10−10 exp − cm3molecule−1s−1 (Eq. 4.5) 4.1 T [K] ! 1804 k = 2.43 × 10−10 exp − cm3molecule−1s−1 (Eq. 4.6) 4.2 T [K] ! 1801 k = 3.17 × 10−10 exp − cm3molecule−1s−1 (Eq. 4.7) 4.3 T [K]

Eq. 4.5, Eq. 4.6, and Eq. 4.7 are valid for approximately the temperature range 880 to 1360 K. The individual data points are listed in Tables 4.1, 4.2, and 4.3 for n-pentane, n-heptane, and n-nonane, respectively. These data are shown in Figure 4.4. 4.4. RESULTS 57

1250 K 1000 K 833 K ] 10 -1

s 9

-1 8 7 n-no 6 nane +OH 5 molecule 3 n-h 4 n-pe epta nta ne+O cm ne H +OH -11 3 [10 2 (4.1) C H + OH -> C H + H O 5 12 5 11 2

-alkane+OH (4.2) C H + OH -> C H + H O 7 16 7 15 2 n k (4.3) C H + OH -> C H + H O 9 20 9 19 2 1 0.7 0.8 0.9 1.0 1.1 1.2 1000/T [1/K]

Figure 4.4: Measured rate constants for Reactions (4.1), (4.2), and (4.3), reactions of OH with n- pentane, n-heptane, and n-nonane, respectively, inferred from the measured OH time-histories using the kinetic modeling method. Solid lines are the Arrhenius ﬁts to the data. The error bars represent the results of a detailed uncertainty analysis.

The magnitudes of the rate constants follow the same order the n-alkane size, with

Reaction (4.1) the slowest and n-pentane having the fewest carbon atoms (C5), and

Reaction (4.3) the fastest and n-nonane having the most carbon atoms (C9). This is expected since the larger n-alkane has more hydrogen-atom abstraction sites for the reaction to occur. n-Heptane has four more hydrogen atoms than n-pentane, and these hydrogen atoms are bonded to secondary carbon atoms, and n-nonane has four more hydrogen atoms than n-nonane, also on secondary carbon atoms; therefore, the difference between the measured rate constants for Reactions (4.1), (4.2), and (4.3) can yield information about the rate of reaction at secondary carbon abstraction sites, provided that the differences in neighboring atom effects is negligible. This type of strategy is how empirical additivity methods can be developed to estimate rate constants for reactions in the family of n-alkane+OH. Further discussion on additivity methods is presented in Section 4.5.2, where an existing additivity model is shown to predict the current data well. Additional discussion on additivity models is also presented in Appendix D. 58 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

Table 4.1: Individual data points ﬁt using the alkane/TBHP mechanism for the rate constant for

Reaction (4.1): C5H12 + OH −−→ C5H11 + H2O.

3 −1 −1 Mixture T [K] P [atm] k4.1 [cm molecule s ]

−11 303 ppm C5H12, 1364 0.84 4.90×10 12 ppm TBHP, 1253 0.93 4.07×10−11 Argon 1196 1.20 3.82×10−11 1077 1.35 3.07×10−11 874 1.24 2.16×10−11

−11 211 ppm C5H12, 1320 0.85 4.57×10 14 ppm TBHP, 1182 0.96 3.74×10−11 Argon 1091 1.02 3.16×10−11 1025 1.08 2.82×10−11 960 1.18 2.57×10−11

−11 200 ppm C5H12, 1291 0.74 4.40×10 20 ppm TBHP, 1282 0.87 4.23×10−11 Argon 1190 0.82 3.82×10−11 1186 0.94 3.74×10−11 1058 0.94 2.82×10−11 1002 1.12 2.90×10−11 869 1.27 1.99×10−11

−11 197 ppm C5H12, 1225 0.94 4.15×10 13 ppm TBHP, 1221 0.96 3.99×10−11 Argon 1164 0.99 3.65×10−11 917 1.24 2.24×10−11 892 1.28 2.16×10−11

Table 4.2: Individual data points ﬁt using the alkane/TBHP mechanism for the rate constant for

Reaction (4.2): C7H16 + OH −−→ C7H15 + H2O.

3 −1 −1 Mixture T [K] P [atm] k4.2 [cm molecule s ]

−11 206 ppm C7H16, 1364 0.842 6.73×10 12 ppm TBHP, 1112 1.020 4.65×10−11 Argon 1101 1.014 4.48×10−11 1083 1.047 4.57×10−11 939 1.155 3.49×10−11

−11 198 ppm C7H16, 1187 0.966 5.40×10 15 ppm TBHP, 1099 1.047 4.65×10−11 Argon 970 1.157 3.90×10−11 892 1.233 3.32×10−11 869 1.254 2.99×10−11

−11 150 ppm C7H16, 1216 0.927 5.48×10 15 ppm TBHP, 1165 0.993 5.06×10−11 Argon 1159 1.928 5.06×10−11 1077 2.060 4.57×10−11 1055 1.054 4.48×10−11 992 1.128 3.99×10−11 4.4. RESULTS 59

Table 4.3: Individual data points ﬁt using the alkane/TBHP mechanism for the rate constant for

Reaction (4.3): C9H20 + OH −−→ C9H19 + H2O.

3 −1 −1 Mixture T [K] P [atm] k4.3 [cm molecule s ]

−11 214 ppm C9H20, 1352 0.874 8.64×10 16 ppm TBHP, 1330 0.855 8.30×10−11 Argon 1124 0.990 5.98×10−11 1103 1.071 6.48×10−11 975 1.170 4.81×10−11 937 1.201 4.65×10−11 884 1.263 4.31×10−11

−11 168 ppm C9H20, 1246 0.939 7.31×10 16 ppm TBHP, 1167 1.003 6.48×10−11 Argon 1154 1.010 7.06×10−11 1021 1.126 5.31×10−11

4.4.2 Uncertainty Analysis

A detailed uncertainty analysis, accounting for uncertainty in temperature, pressure, initial TBHP concentration, initial n-alkane concentration, laser intensity, data fitting, impurities, reaction products, and the rate constants of the four most important secondary reactions, was performed for an experiment with n-nonane at 1167 K. The influence of uncertainties in each of these parameters on the uncertainty of the rate constant for Reaction (4.3) was obtained by perturbing each uncertainty source to its 2σ error bounds and redetermining the best-fit rate constant for Reaction (4.3). Figure 4.5 shows the contribution from each source of uncertainty considered to the overall uncertainty of the rate constant for the Reaction (4.3) determined using the kinetic modeling method in this work. The primary contributions to the overall uncertainty include the fitting of the model to the experimental data trace, and the initial transmitted laser intensity. Secondary contributions to the uncertainty are the initial fuel concentration and the rate constant for Reaction (3.3), which were minimized through laser absorption measurements at 3.39 µm and measurement of OH decay in neat TBHP experiments, respectively. The uncertainties presented in Figure 4.5 were assumed to be uncorrelated, and these uncertainties were combined in a root- sum-squared method to yield a total uncertainty in the rate constant measurement. At 1167 K, the estimated overall uncertainty in the rate constant for Reaction (4.3) is ±11%, and this uncertainty estimate is approximately valid for each of the rate 60 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

constants for Reaction (4.1), (4.2), and (4.3) in the temperature range from 1000 to 1364 K. For temperatures below 1000 K, the inﬂuence of the uncertainty of the rate constant for Reaction (3.1) in the ﬁnal rate constant determinations increases with decreasing temperatures, leading to a maximum uncertainty of ±23% at 869 K for each of the rate constants for Reaction (4.1), (4.2), and (4.3).

1167 K, 1.00 atm 168 ppm C9H20, 16.0 ppm TBHP

Uncertainty source (+/- 2σ uncertainty) Temperature (+/- 1%) Pressure (+/- 1%) OH absorption coefficient (+/- 3%) Wavelength (+/- 0.032 cm-1 in UV) TBHP adsorption or decomposition in mixing tank (max 10%) n-Alkane concentration (+/- 5%) Laser intensity (+/- 0.15%) Fitting (+/- 7%) Time zero (+/- 1.5 μs) Impurities (+1 ppm H) Branching ratio of n-alkane+OH (3.1) (CH ) COOH -> (CH ) CO + OH (+/- 30%) 3 3 3 3 (3.3) CH + OH -> CH (s)+H O (+/- 30%) 3 2 2 CH +OH(+M) -> CH OH(+M) (uncertainty factor 2) 3 3 CH +CH (+M) -> C H (+M) (uncertainty factor 2) 3 3 2 6

-10-50 5 101520 Contribution to uncertainty in k [%] 4.3 Overall RSS uncertainty: 1 Reaction (4.3): C H + OH -> C H + H O +/- 11% 9 20 9 19 2 1

Figure 4.5: Factors considered in the uncertainty analysis for the rate constant for Reaction (4.3) at 1167 K, 1.00 atm. Each error source is listed with its 2σ uncertainty bound which was propagated into the ﬁnal rate constant determination. The overall uncertainty of ±11% for the rate constant for Reaction (4.3) at 1167 K is determined using a root-sum-squares combination of the individual uncertainty contributions.

4.5 Comparisons with Literature

4.5.1 Previous Experimental Works

Cohen and coworkers [6, 7, 9] pioneered the use of TBHP as an OH precursor to study the rate constants for reactions in the family of n-alkane+OH at temperatures near 4.5. COMPARISONS WITH LITERATURE 61

1100 K in the 1980’s. Koffend and Cohen [9] used OH absorption near 310 nm generated from a microwave discharge, and monitored the OH mole fraction exponential decay time-constant for multiple single-temperature experiments with varying initial OH mole fractions to determine an overall n-alkane+OH rate constant for n-heptane and n-nonane. The single-temperature rate constant measurements of Koffend and Cohen for n-heptane+OH and n-nonane+OH are 28% and 26% slower, respectively, than the current data. Though Koffend and Cohen only claimed to measure the rate constant value at a single temperature, their reported rate constant is an average over many experiments which span a temperature range of approximately 100 K surround- ing the average temperature reported for the measured rate constant, and their data for the repeated experiments exhibit high scatter. Both of these factors are likely to contribute to the discrepancy of their results with the current measurements. While the rate constants of Koffend and Cohen are fit from high-scatter data, their work was the first to show the relationship between the high-temperature rate constants of the reactions of OH with n-heptane and n-nonane, which show that the rate constant involving n-nonane is faster by approximately 30%. The current measurements also illustrate this relationship to hold true.

High-temperature measurements for n-alkane+OH reaction rate constants have also been recently performed by Sivaramakrishnan and Michael [11] to yield rate constant measurements as a function of temperature for a set of large alkanes, including n-pentane and n-heptane. Their work employed a technique similar to the current work with TBHP and shock tubes. In the work of Sivaramakrishnan and Michael, very dilute mixtures of an alkane and TBHP in argon (on the order of tens of ppm) were used with an initial alkane-to-TBHP concentration ratios averaging ten for experiments with n-pentane, but only averaging six for experiments with n-heptane. The OH time-histories of Sivaramakrishnan and Michael were monitored using multi-pass absorption of light from an OH resonance lamp, and all rate constant determinations were performed with a pseudo-ﬁrst-order analysis, claiming negligible eﬀects of TBHP chemistry, and obtaining overall n-alkane+OH rate constants directly from the time- constant of OH decay. The current measurements for n-pentane and n-heptane are approximatley 20% faster than the data from Sivaramakrishnan and Michael. The 62 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

source of this discrepancy is still unclear. Although Sivaramakrishnan and Michael performed analysis with a detailed kinetic mechanism to conclude that secondary kinetics from Reactions (3.3) and (3.4) did not effect the OH concentrations under their experimental conditions, the rate constant they used for Reaction (3.3) was ∼50% slower than the rate constant determined in Chapter 3 of this thesis. Hence, the TBHP kinetic effects on the OH concentration likely were non-negligible. However, an analysis using the current kinetic mechanism to account for secondary chemistry on the OH time-histories from Sivaramakrishnan and Michael’s experiments would only serve to widen the discrepancy between their rate constant measurements and the current work. Other parameters which can commonly cause this sort of systematic error seen between the data sets include the presence of impurities, or alkane loss due to adsorption or condensation onto the facility surfaces. The absence of impurities and the initial composition of the test mixtures used in the current experiments were each verified using different laser absorption techniques, as described in Chap- ter 2, and any uncertainties were accounted in the detailed error analysis described in Section 4.4. If an analysis of systematic errors for the work of Sivaramakrishnan and Michael were to be conducted, it is likely that their rate constant measurements would have overlapping uncertainty limits with the present work. The current data obtained for the overall rate constants for Reactions (4.1), (4.2), and (4.3) in this study are shown in Figure 4.6 in comparison with the data of Koffend and Cohen [9] and Sivaramakrishnan and Michael [11]. Also shown are a few estimated rate constants which are discussed in Section 4.5.2. To the author’s knowledge, the data taken for the rate constant for Reaction (4.3) are the first measurements showing the temperature-dependence of the rate of OH reaction with n-nonane at combustion- relevant temperatures.

4.5.2 Validation of Estimation Methods

The current rate constant measurements describe the overall rate constant for each n-alkane+OH reaction, though several diﬀerent abstraction sites are possible for each 4.5. COMPARISONS WITH LITERATURE 63

1250 K 1000 K 833 K 10 9 8 ]

-1 7 s 6 -1 5 4 n-nonane

molecule 3 n-heptane 3 -alkane+OH n k cm n-pentane

-11 2 [10 Red: (4.1) C5H12 + OH -> C5H11 + H2O

Green: (4.2) C7H16 + OH -> C7H15 + H2O Blue: (4.3) C H + OH -> C H + H O 1 9 20 9 19 2 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1000/T [K-1]

High-Temperature Data Estimation Methods Current Work IGS - Srinivasan and Michael (2009) C H C H C H Sivaramakrishnan 5 12 7 16 9 20 and Michael (2009) SAR - Kwok and Atkinson (1995) Koffend and Cohen C H C H C H (1996) 5 12 7 16 9 20

]

Low-Temperature Data -1 400 K 333 K 285 K

s 1.8

Darnall et al. -1 (1978) 1.4 Nolting et al. (1988) Abbatt et al. (1990) 1

Talukdar et al. molecule 3 (1994)

Ferrari et al. (1996) cm 0.6 Donahue et al. -11 [10

(1998) Coeur et al. (1998) DeMore and Bayes -alkane

(1999) n Colomb et al. (2004) 0.2

Li et al. (2006) OH+ k 2.5 3.0 3.5 4.0 Wilson et al. (2006) 1000/T [K-1]

Figure 4.6: Measured rate constants for Reactions (4.1), (4.2), and (4.3), reactions of OH with n- pentane, n-heptane, and n-nonane, respectively, from the current work compared with data [72–82] and estimation methods [11, 22] from the literature for (main plot/top) high temperatures 800 to 1300 K, and (bottom right) low temperatures 250 to 440 K. 64 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

reaction, leading to different isomers of the radical product. While the current experimental results do not yield information about the relative rate constants of the different abstraction channels (the rate constant determination is independent of the branching ratios between the different abstraction sites), several different types of estimation methods lead to determination the rate constants of n-alkane+OH for each abstraction site, and the accuracy of these methods can be determined by comparing the measured results with the estimated overall rate constant for the n-alkane+OH reaction, obtained by summing over all the product channels.

Estimation methods capable of site-specific rate constant predictions have existed since Greiner [19] developed the first additivity model in 1970. Since then, others have developed similar models [23], improved additivity models which include carbon neighbor interactions [11, 20–22, 82], and other estimation methods employ transition- state theory [24, 25] and incorporate reaction-class factors obtained through linear energy-relationships [26]. These estimation methods can be used to determine the relative branching ratios leading to different product channels, information which is useful in developing detailed kinetic mechanisms. Further information on determining site-specific rate constants using these estimation methods is described in Appendix D, and comparisons to two of the most recent of them will be discussed here.

The improved group scheme (IGS) by Sivaramakrishnan and Michael [11] applies additivity principles for predicting n-alkane+OH reaction rate constants, and uses a large experimental database for n-alkanes for molecules as large as n-heptane. Sivaramakrishnan and Michael’s empirical IGS ascribes a different rate constant for hydrogen-atom abstraction by OH at each different carbon center dependent on carbon interactions from neighbors up to the next-next-nearest neighbor. While Sivara- makrishnan and Michael developed the IGS to fit their experimental data for n- alkanes as large as n-heptane, only a single temperature data point for n-nonane+OH was available from Koffend and Cohen [9] for validation of the scheme for larger n- alkanes. The IGS comes close to predicting the rate constant for the n-nonane+OH reaction around 900 K; however, the rate constant measurements for n-nonane+OH for temperatures of 884 to 1352 K in the current study show a steeper temperature 4.5. COMPARISONS WITH LITERATURE 65

dependence than predicted by the IGS, as can be seen in Figure 4.6. The use of Kof- fend and Cohen’s [9] n-heptane+OH rate constant measurement in determining the parameters for the IGS is at least partially responsible for the discrepancy between the rate constant predictions by the IGS and the current measurements. As discussed in Section 4.5.1 and evident in Figure 4.6, the Koffend and Cohen rate constant for n-heptane+OH is slower than both the current measurements and measurements of Sivaramakrishnan and Michael for the same reaction. Furthermore, the abstract of the Koffend and Cohen paper incorrectly reports the temperature of their n-heptane+OH rate constant measurement as 1186 K, and Sivaramakrishnan and Michael appear to have used this temperature for this data point in their modeling (Table III in the Koffend and Cohen text clearly reports 30 individual data points at temperatures which average to 1086 K for their n-heptane experiments). Therefore, the attempt of Sivaramakrishnan and Michael to include the Koffend and Cohen n-heptane+OH rate constant measurement in the development of an estimation method for the rate constants for n-alkane+OH reactions would result in rate constant estimations which would be too slow near 1186 K. The additivity estimation methods by Atkinson and coworkers [20–22] are termed structure-activity relationships (SAR) which ascribe a rate constant for hydrogen- atom abstraction by OH for each primary, secondary, and tertiary carbon site. The SAR estimation accounts for neighboring atom effects by lowering the activation energy of the H-atom abstraction at each carbon site, depending on the identity of the neighboring atom, and the degree of the activation energy change is determined through examining literature databases for data from 250 to 1000 K. While the most recent SAR values updated by Kwok and Atkinson [22] were developed for temperatures from 250 to 1000 K, this updated SAR estimation precisely predicts the rate constants for the n-alkane+OH reactions measured in this study up to 1364 K for all three of the alkanes (n-pentane, n-heptane, and n-nonane) and fits the temperature dependence well. While both the improved group scheme of Sivaramakrishnan and Michael [11] and the updated structure-activity relationship from Kwok and Atkinson [22] are adequate at predicting the overall n-alkane+OH rate constants for n-pentane, n-heptane, and 66 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES

n-nonane at temperatures from 250 to 440 K [72–82], as shown in Figure 4.6, only the SAR estimation of Kwok and Atkinson correctly predicts the temperature dependence for the overall rate constant for n-alkane+OH from the data in the current work at temperatures greater than 800 K.

4.6 Conclusions

The overall rate constants for Reactions (4.1), (4.2) and (4.3), describing reactions of OH with n-pentane, n-heptane, and n-nonane, respectively, were studied behind reflected shock waves by using tert-butylhydroperoxide (TBHP) to generate OH radicals in mixtures with each n-alkane dilute in argon to yield pseudo-first-order kinetics in OH. OH time-histories were monitored using narrow-linewidth laser absorption near 306.7 nm, and the results were examined using both a pseudo-first-order analysis and with a detailed kinetic mechanism that was developed to account for both TBHP and n-alkane kinetics. The current rate constant measurements show agreement within 20% with those measured by Sivaramakrishnan and Michael [11] for n-pentane and n-heptane, and provide the first known temperature-dependent rate constant measurements for n-nonane+OH above 800 K. Systematic errors due to impurities and uncertainty in mixture composition were minimized with laser absorption measurements verifying the absence of impurities and confirming accurate knowledge of the initial n-alkane composition, leading to an overall uncertainty in the rate constant measurements of ±11% for temperatures from 1000 to 1364 K. The overall uncertainty in the rate constant determination increases with decreasing temperature below 1000 K, up to ±23% at 869 K. The current rate constant measurements for Reactions (4.1), (4.2) and (4.3) were compared to two recent estimation methods from the literature for predicting rate constants of reactions in the family of n-alkane+OH. The most recent improved group scheme model of Sivaramakrishnan and Michael [11], developed from data using normal alkanes of C7 and smaller, fails to predict the temperature dependence of the current n-nonane+OH reaction rate constant measurements at temperatures above 800 K. The structure-activity relationship model developed by Atkinson [20, 21], 4.6. CONCLUSIONS 67

updated with parameters by Kwok and Atkinson [22], was developed using data in the temperature range 250 to 1000 K, and is shown to well-predict the current n- alkane+OH rate constant data taken for n-pentane, n-heptane, and n-nonane, even up to 1364 K. 68 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES Chapter 5

Reaction of OH with n-Butanol

5.1 Introduction

5.1.1 Background and Motivation

In 2006, DuPont and BP announced a partnership to begin production of n-butanol

(1-butanol: CH3CH2CH2CHOH) from biomass, also referred to as biobutanol, because of the advantages of biobutanol over ethanol for use as a fuel additive or alternative fuel [28]. In the years following, efforts towards developing detailed chemical kinetic models for high-temperature combustion of n-butanol have expanded rapidly to support the introduction of biobutanol into the transportation sector. According to Moss et al. [31], the reaction of OH with n-butanol is a major fuel consumption pathway during combustion of n-butanol. Therefore, the rate constant for this reaction must be known well to develop an accurate detailed kinetic mechanism for n-butanol combustion. The abstraction of a hydrogen atom from n-butanol by OH can proceed through five different reaction channels which result in different product species, as described by Reactions (5.1a) through (5.1e). The products of Reactions (5.1a) through (5.1d) consist of a water molecule and a 1-hydroxy-butyl radical, the latter of which can exist in four isomers; this thesis will use a naming con- vention which denotes different isomers of the 1-hydroxybutyl radicals by their radical position relative to the hydroxyl group. For example, Reaction (5.1a) produces an

69 70 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

the α-radical (1-hydroxy-but-1-yl: CH3CH2CH2CHOH), Reaction (5.1b) produces an 1 the β-radical (1-hydroxy-but-2-yl: CH3CH2CHCH2OH), and so on. The products of Reaction (5.1e) consist of a water molecule and a 1-butoxyl radical.

CH3CH2CH2CH2OH + OH −→ CH3CH2CH2CHOH + H2O (5.1a)

−→ CH3CH2CHCH2OH + H2O (5.1b)

−→ CH3CHCH2CH2OH + H2O (5.1c)

−→ CH2CH2CH2CH2OH + H2O (5.1d)

−→ CH3CH2CH2CH2O + H2O (5.1e)

Early detailed kinetic mechanisms of n-butanol combustion included site-specific rate constants for Reactions (5.1a) through (5.1e) that were estimated from analogous reactions with alkanes or ethanol [29–32]. The mechanism of Black et al. [85] used additional knowledge from theoretical calculation of the individual bond energies in the n-butanol molecule to estimate the site-specific rate constants for Reactions (5.1a) through (5.1e). The mechanism of Grana et al. [40] used estimations for the rate constants for Reactions (5.1a) through (5.1e) made with the basis of a systematic approach for similar reactions of hydrocarbon species [86], while also considering quantum calculations of Galano et al. [87] for reactions of OH with alcohols. Recently, studies focusing directly on the high-temperature rate constant for the reaction of OH with n-butanol have been undertaken, including high-temperature experimental measurements [47] and ab initio studies with high-level electronic structure calculations [88]. Vasu et al. [47] conducted the first high-temperature measurements of the overall rate constant2 for Reaction (5.1) using tert-butylhydroperoxide (TBHP) as a fast OH precursor in shock tube experiments in the temperature range 1017 to

1The terms α-radical, β-radical, and γ-radical will be used in the subsequent chapters in this thesis to refer to different radicals. In all cases, the Greek letter distinguishes the position of the radical with respect to the hydroxyl group on the butanol radical isomer of the respective chapter. 2Reactions with the same reactants but different products will be labeled with same reaction number, appended with different letters of the alphabet. The term “overall reaction” will be used to refer to the overall reaction of the reactants, including all product channels. Reference to the reaction number without any letters always refers to the overall reaction. The rate constant for the overall reaction is always defined as the sum of the site-specific rate constants, similar to in Eq. 5.1. 5.1. INTRODUCTION 71

1269 K. Their measurements yielded only the overall rate constant, which is related to the site-speciﬁc rate constants by Eq. 5.1.

k5.1 = k5.1a + k5.1b + k5.1c + k5.1d + k5.1e (Eq. 5.1)

Studies focusing on the site-specific rate constants for Reactions (5.1a) through (5.1e) include ab initio calculations, such as those published by Zhou et al. [88]; confidence in ab initio rate constant calculations is typically gained by comparison of the calculated overall rate constant, determined by Eq. 5.1, with experimental data. Experimental measurements are necessary to investigate the validity of ab initio calculations, though the reported rate constants of Vasu et al. [47] can be sensitive to kinetic modeling. As numerous advances in the kinetic modeling of n-butanol have occurred since the work of Vasu et al., the influences of kinetic modeling on the determination of the rate constant for Reaction (5.1) need to be examined.

5.1.2 Objectives of the Current Chapter

The sensitivity of the experimental rate constant reported by Vasu et al. [47], together with recent improvements in the kinetic modeling of the OH precursor (from Chap- ter 3) and n-butanol [36, 40, 85, 89], draws attention to deficiencies in the analysis of Vasu et al., causing concerns about the accuracy of their experimental data and the reported rate constant. Furthermore, the temperature range studied by Vasu et al. (1017 to 1269 K) provides limited confidence in the temperature dependence of the rate constants obtained by ab initio calculations for combustion-relevant conditions. These two concerns motivate the work presented in this chapter. This chapter examines effects of discrepancies in kinetic modeling for both TBHP decomposition and n-butanol chemistry on the determination of the rate constant for Reaction (5.1) from the experimental data of Vasu et al. [47]. In addition, new experiments were also conducted to extend the experimental database of rate constant measurements for Reaction (5.1) to lower combustion-relevant temperatures (to 900 K), to enable validation of rate constants for this reaction calculated using ab initio methods over a wider temperature range. 72 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

The results presented in this chapter include rate constant measurements in shock tube experiments at temperatures from 900 to 1200 K where laser absorption by OH was carried out behind reflected shock waves in mixtures of tert-butylhydroperoxide (TBHP) and n-butanol dilute in argon. A detailed kinetic mechanism was constructed to include updated rate constants of all reactions of TBHP and n-butanol which influence the near-first-order OH concentration decay under the experimental conditions; this mechanism was used as the final analysis tool for the determination of the overall rate constant for Reaction (5.1) in this chapter. The measured overall rate constant for Reaction (5.1) is compared to previously published experimental data [47], ab initio calculations [88], and a structure-activity relationship [20–22, 90].

5.2 Analysis of n-Butanol Kinetic Mechanisms

Chapter 4 revealed that kinetic modeling was necessary in the analysis of experiments using TBHP as an OH precursor to determine the rate constant for reactions of OH with an organic compound. The kinetic mechanism used for analysis must include reactions and rate constants describing TBHP decomposition, and also a base mechanism describing other secondary reactions that would be expected to occur following the reaction of interest. In the work of Vasu et al. [47], they used a kinetic mechanism based on n-butanol kinetics from the work of Sarathy et al. [32] to determine the rate constant for Reaction (5.1) from measured OH time-histories under experimental conditions for near-pseudo-ﬁrst-order kinetics. In this section, the inﬂuence of changes in kinetic modeling on the analysis of the Vasu et al. data will be examined, and the kinetic mechanism used for the analysis in this chapter will be presented.

5.2.1 Inﬂuence of TBHP Kinetics

For the analysis in their work, Vasu et al. [47] used the n-butanol mechanism from Sarathy et al. [32] with Reactions (3.1) and (3.2) added, reactions describing the decomposition of TBHP and the tert-butoxyl radical, respectively. The rate constants 5.2. ANALYSIS OF N-BUTANOL KINETIC MECHANISMS 73

Vasu et al. used for Reactions (3.1) and (3.2) are similar to those discussed in Chap- ter 3. As shown in Figure 5.1, the mechanism used by Vasu et al. does not correctly predict the OH time-histories of TBHP decomposition that were measured in Chap- ter 3. Therefore, their mechanism does not correctly account for secondary reactions associated with TBHP decomposition, and these errors were likely propagated into their determination of the rate constant for Reaction (5.1).

1158 K, 1.10 atm 928 K, 1.22 atm 20 20 20 ppm TBHP, argon 20.5 ppm TBHP, argon

16 16

12 12

8 8

4 4 Data (from Chapter 3) OH mole fraction [ppm] Vasu et al. (2010) 0 Modified Vasu et al. (see text) 0

0 20406080100 0 204060 Time [s]

Figure 5.1: Measured OH time-histories from Chapter 3 for experiments of dilute mixtures of TBHP in argon. Also shown are simulated OH time-histories using the mechanism used for analysis by Vasu et al. [47] and a modiﬁed version of the Vasu et al. mechanism with the rate constants presented in Table 3.1. Conditions are (left) 1158 K, 1.10 atm for 20.0 ppm TBHP, argon and (right) 928 K, 1.22 atm for 20.5 ppm TBHP, argon.

The rate constant for the reaction of OH with methyl radicals, Reaction (3.3), in the mechanism of Vasu et al. [47] (from the Sarathy et al. [91] mechanism) is over an order of magnitude slower than the rate constant determined in Chapter 3 of this work for the same reaction. This discrepancy is the leading cause of the inability of the mechanism used by Vasu et al. to correctly predict the measured OH time-histories during TBHP decomposition. If the rate constants of the reactions in Table 3.1 were used in the mechanism of Vasu et al., their mechanism would correctly predict the measured OH time-histories during neat TBHP decomposition, as shown in Figure 5.1. The resulting mechanism obtained by updating the rate constants in 74 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

the mechanism of Vasu et al. with the rate constants presented in Table 3.1 will be referred to as the modified Vasu et al. mechanism in this chapter. The modified Vasu et al. mechanism was used to determine the rate constant for Reaction (5.1) from the measured OH time-histories of Vasu et al. [47] at their highest and lowest temperature data points. Similar to the analysis used by Vasu et al., in the current analysis with the modified mechanism, the rate constant for Reaction (5.1b) was preserved and only the sum of the rate constants for Reac- tions (5.1a), (5.1c), (5.1d), and (5.1e) was varied to determine the overall rate constant for Reaction (5.1). The results are shown in Figure 5.2 in comparison to the published rate constants presented by Vasu et al., illustrating that the inadequate modeling of the OH time-history during TBHP decomposition using the Vasu et al. mechanism leads to a discrepancy of approximately 10%.

Reaction (5.1): CH CH CH CH OH + OH -> Products 3 2 2 2 1250 K 1111 K 1000 K 5 ] -1 s

-1 4

3 molecule 3 cm

-11 2

[10 Kinetic mechanism used for analysis:

5.1 Vasu et al. (2010) k Modified Vasu et al. (2010) Modified Grana et al. (2010) Modified Sarathy et al. (2012) 1 0.75 0.80 0.85 0.90 0.95 1.00 1000/T [K-1]

Figure 5.2: Arrhenius plot of the rate constant for Reaction (5.1) determined from the measured OH time-histories in the work of Vasu et al. [47]. The rate constant for Reaction (5.1) was determined by fitting simulated OH time-histories using the different mechanisms [40, 47, 91] noted the legend to the measured traces. Each mechanism label “Modified” contains the reactions and rate constants presented in Table 3.1 (see text in Section 5.2.2). The error bars shown on the reported data of Vasu et al. represent their reported uncertainty of ±14%. 5.2. ANALYSIS OF N-BUTANOL KINETIC MECHANISMS 75

5.2.2 Sensitivity of k5.1 Determination to Mechanism

Numerous detailed kinetic mechanisms for n-butanol combustion can be found in the literature today. The first models appeared in the literature in 2008 when Da- gaut and coworkers [29, 30] and Moss et al. [31] each published separate mechanisms, using data from a jet-stirred reactor and shock tube ignition delay times, respectively, as validation targets. Researchers from around the world quickly followed suit, adding to the literature additional and revised n-butanol mechanisms developed from new experimental validation targets [32, 34, 36, 40, 85, 89, 91]. Each of these n-butanol mechanisms can be modified to include TBHP chemistry by adding the Reactions (3.1) and (3.2) with the respective rate constants in Table 3.1. Further- more, updating the rate constants for Reactions (3.3) and (3.4) in each mechanism with the values listed in Table 3.1 typically leads the mechanism to correctly simulate the measured OH time-histories in the neat TBHP experiments from Chapter 3. The n-butanol mechanisms from the works of Grana et al. [40] and Sarathy et al. [91] (different from the mechanism of Sarathy et al. [32] that was used in the Vasu et al. [47] analysis) were modified to include TBHP chemistry in the manner described above, and used to analyze the measured OH time-histories of Vasu et al. at their highest and lowest temperature data point. The rate constant determination can be sensitive to the branching ratios of Reaction (5.1), therefore, the branching ratios for the overall reaction excluding the Reaction (5.1b) channel (i.e. k5.1a/(k5.1a + k5.1c + k5.1d + k5.1e), etc.) specified in each mechanism were preserved in the analysis, and the sum of k5.1a + k5.1c + k5.1d + k5.1e was varied to adjust the simulated OH time-history fit while the rate constant for Reaction (5.1b) from each respective mechanism was preserved. The resulting overall rate constant for Reac- tion (5.1) determined from these different mechanisms is shown in Figure 5.2. A peak-to-peak discrepancy of ∼30% is found for the rate constant determined for Re- action (5.1), depending on which base mechanism for n-butanol kinetics was used. This discrepancy is due entirely to differences in the kinetic mechanisms because the same OH time-histories from the work of Vasu et al. were used as the starting point of the analysis. The discrepancy is larger than the overall uncertainty limit of ±14% determined by Vasu et al., suggesting that their uncertainty analysis did not adequately 76 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

account for uncertainties in the secondary kinetics. Many reactions and rate constants in the mechanisms used for the analysis of the Vasu et al. [47] data diﬀer, and a few key rate constants that contribute to this discrepancy can be elucidated by examining the reaction pathways of n-butanol after reaction with OH, as shown in Figure 5.3. These include the following types of reactions:

1. Reactions of n-butanol, including bimolecular reactions with OH and H radicals, such as Reactions (5.1) and (5.2).

CH3CH2CH2CH2OH + H −→ CH3CH2CH2CHOH + H2 (5.2a)

−→ CH3CH2CHCH2OH + H2 (5.2b)

−→ CH3CHCH2CH2OH + H2 (5.2c)

−→ CH2CH2CH2CH2OH + H2 (5.2d)

−→ CH3CH2CH2CH2O + H2 (5.2e)

2. Reactions of 1-butoxyl and hydroxybutyl radicals, including unimolecular beta- scission decomposition reactions and unimolecular isomerization reactions, such as Reactions (5.3) through (5.7).

CH3CH2CH2CHOH −→ C2H5 + CH2−CHOH (5.3a)

−→ CH2CH2CH2CH2OH (5.3b)

CH3CH2CHCH2OH −→ 1− C4H8 + OH (5.4a)

−→ CH3 + CH2−CHCH2OH (5.4b)

CH3CH2CHCH2OH −→ CH2OH + C3H6 (5.5a)

−→ CH3CH2CH2CH2O (5.5b)

CH2CH2CH2CH2OH −→ CH2CH2OH + C2H4 (5.6a)

−→ CH3CH2CH2CH2O (5.6b)

CH3CH2CH2CH2O −→ CH2CH2CH3 + CH2O (5.7) 5.2. ANALYSIS OF N-BUTANOL KINETIC MECHANISMS 77

3. Reactions of smaller n-butanol radical fragments, including bimolecular reactions with OH radicals and unimolecular beta-scission decomposition reactions, such as Reactions (5.8) through (5.13).

C2H5 + OH −→ C2H4 + H2O (5.8a)

−→ CH3 + CH2O + H (5.8b)

−→ C2H5OH (5.8c)

CH2OH + OH −→ CH2O + H2O (5.9)

CH2CH2OH + OH −→ C2H4O + H2O (5.10)

C2H5 −→ C2H4 + H (5.11)

CH2OH −→ CH2O + H (5.12)

CH2CH2OH −→ C2H4 + OH (5.13)

(5.1a) OH (5.1e) 33% 2% +OH (5.1d) (5.1b) (5.1c) +OH 34% 8% 23% +OH H O+ +H2O 2 +OH +OH OH (5.3b) O α-radical (5.6b) 1-butoxyl (5.3a) (5.5b) +H2O (5.7) +H2O +H2O OH OH OH δ-radical +CH2CHOH β-radical γ -radical (5.6a) +CH2O (5.4a) (5.4b) (5.5a) (5.11) (5.8) +OH +C2H4 +C3H6 OH +OH OH CH3 C H +H O +1-C H OH C2H4+H 2 4 2 4 8 +C3H5OH (5.13) CH +CH O+H 3 2 (5.12) (5.9) C2H4+CH3 C3H6+H2O C2H5OH +OH OH-consuming reaction C2H4+OH OH-producing secondary reaction Other secondary reaction CH2O+H CH2O+H2O

Figure 5.3: Reaction pathways important in the calculation of OH time-history under the current experimental conditions. Reactions involved in OH consumption are red and reactions involved in OH production are green. The relative magnitudes of the rate constants to diﬀerent product channels of Reaction (5.1) at 1197 K are illustrated by the thickness of the reaction arrow. The branching ratios for Reaction (5.1) from Zhou et al. [88] are listed next to the arrows. 78 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

Diﬀerences in the rate constants for Reactions (5.2) through (5.13) in the various mechanisms examined [32, 40, 47, 91] lead to the large discrepancies seen in the determination of the rate constant for Reaction (5.1) from the same raw data (as shown in Figure 5.2). Therefore, a mechanism with accurate rate constants for important reactions must be carefully chosen, or constructed, for the analysis of the measured OH time-histories for the determination of the rate constant for Reaction (5.1). Fur- ther discussion on the important secondary reactions that inﬂuence the simulated OH time-history is presented in Section 5.5.

5.2.3 Mechanism Generation for Current Work

A detailed kinetic mechanism was constructed to include secondary reactions of importance involving both TBHP and n-butanol kinetics, using the current best-known rate constants for key reactions. The alkane/TBHP mechanism presented in Chap- ter 3 was used as the starting point; this base mechanism includes alkane kinetics from the JetSurF 1.0 mechanism [18] and added reactions shown to accurately describe measured OH time-histories during TBHP decomposition. Reactions (5.2) through (5.13) were added to the alkane/TBHP mechanism; many of these added reactions are shown in Figure 5.3. Thermodynamic data for all new chemical species added to the base mechanism were taken from Sarathy et al. [91] who used the THERM program [92] to calculate temperature-dependent enthalpy and entropy values. Rate constants for Reactions (5.2) through (5.13) were taken from recent literature experiments and calculations [91, 93–99], and the rate constant values are listed in Table 5.1. A method based on the work of Curran [100] was used to estimate rate constants for radical decomposition reactions where appropriate published rate constants could not be found, and a description of this procedure is provided Appendix E. For unimolecular reactions where only the high-pressure-limit rate constant could be found, the variation of the rate constant with pressure was estimated using the Kassel Integral method [99] with S = Smax/2. This method for estimating pressure dependence is also detailed in Appendix E. 5.2. ANALYSIS OF N-BUTANOL KINETIC MECHANISMS 79

Table 5.1: Partial list of reactions and rate constants of the n-butanol/TBHP mechanism of the current work. Units for A are [cm3molecule−1s−1] for bimolecular reactions and [s−1] for unimolecular reactions, units for E are [cal mol−1K−1]. All unimolecular reaction rate constants calculated at 1 atm, and the 3-parameter ﬁts are valid for 800 to 1300 K. f Denotes pressure dependence was estimated from the high-pressure rate constant using the Kassel Integral method [99]. R Denotes rate constant calculated from the reverse rate constant using the mechanism thermodynamic data.

No. Reaction k = A · T b exp(−E/RT ) Reference A b E

13 3 (5.1a) CH3CH2CH2CH2OH + 4.85×10 0.00 3.910×10 This work OH −−→ CH3CH2CH2CHOH + H2O 13 3 (5.1b) CH3CH2CH2CH2OH + 1.41×10 0.00 5.383×10 This work OH −−→ CH3CH2CHCH2OH + H2O 13 3 (5.1c) CH3CH2CH2CH2OH + 3.92×10 0.00 4.319×10 This work OH −−→ CH3CHCH2CH2OH + H2O 14 3 (5.1d) CH3CH2CH2CH2OH + 1.67×10 0.00 7.700×10 This work OH −−→ CH2CH2CH2CH2OH + H2O 12 3 (5.1e) CH3CH2CH2CH2OH + 6.77×10 0.00 7.030×10 This work OH −−→ CH3CH2CH2CH2O + H2O 4 3 (5.2a) CH3CH2CH2CH2OH + 8.79×10 2.68 2.915×10 [91] H −−→ CH3CH2CH2CHOH + H2 5 3 (5.2b) CH3CH2CH2CH2OH + 1.08×10 2.69 4.440×10 [91] H −−→ CH3CH2CHCH2OH + H2 6 3 (5.2c) CH3CH2CH2CH2OH + 1.30×10 2.40 4.471×10 [91] H −−→ CH3CHCH2CH2OH + H2 5 3 (5.2d) CH3CH2CH2CH2OH + 6.66×10 2.54 6.756×10 [91] H −−→ CH2CH2CH2CH2OH + H2 2 3 (5.2e) CH3CH2CH2CH2OH + 9.45×10 3.14 8.701×10 [91] H −−→ CH3CH2CH2CH2O + H2 41 4 f (5.3a) CH3CH2CH2CHOH −−→ C2H5 + CH2−CHOH 7.44×10 -8.59 4.049×10 Appendix E 14 4 f (5.3b) CH3CH2CH2CHOH −−→ CH2CH2CH2CH2OH 1.14×10 -1.08 2.900×10 [94] 27 4 f (5.4a) CH3CH2CHCH2OH −−→ 1- C4H8 + OH 6.95×10 -4.49 3.488×10 Appendix E 34 4 f (5.4b) CH3CH2CHCH2OH −−→ CH3 +CH2−CHCH2OH 5.52×10 -6.33 4.268×10 Appendix E 39 4 f (5.5a) CH3CH2CHCH2OH −−→ CH2OH + C3H6 1.37×10 -7.72 3.943×10 Appendix E 23 4 f (5.5b) CH3CH2CHCH2OH −−→ CH3CH2CH2CH2O 1.40×10 -4.56 3.009×10 [94] 33 4 f (5.6a) CH2CH2CH2CH2OH −−→ CH2CH2OH + C2H4 3.82×10 -6.22 3.354×10 Appendix E 19 4 f (5.6b) CH2CH2CH2CH2OH −−→ CH3CH2CH2CH2O 2.92×10 -2.92 1.756×10 [95] 26 4 (5.7) CH3CH2CH2CH2O −−→ CH2CH2CH3 + CH2O 2.63×10 -4.74 1.295×10 [91] 21 3 (5.8a) C2H5 + OH −−→ C2H4 + H2O 1.31×10 -2.44 3.795×10 [96] 21 3 (5.8b) C2H5 + OH −−→ CH3 + CH2O + H 4.91×10 -2.30 6.477×10 [96] 57 3 R (5.8c) C2H5 + OH −−→ C2H5OH 1.82×10 -13.4 8.795×10 [101] 14 (5.9) CH2OH + OH −−→ CH2O + H2O 1.20×10 0.00 0.00 [96] 13 (5.10) CH2CH2OH + OH −−→ C2H4O + H2O 9.00×10 0.00 0.00 [96] 39 4 R (5.11) C2H5 −−→ C2H4 + H 1.30×10 -7.93 2.482×10 [98] 29 4 (5.12) CH2OH −−→ CH2O + H 2.98×10 -5.57 2.080×10 [96] 41 4 R (5.13) CH2CH2OH −−→ C2H4 + OH 8.22×10 -9.22 1.862×10 [97] 80 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

The mechanism described in this section will be referred to as the n- butanol/TBHP mechanism from hereon in this thesis. While this is not a comprehensive mechanism for describing pyrolysis or oxidation of n-butanol, it does contain all of the reactions that would be expected to influence the OH time-history under the current experimental conditions with the best-known rate constants at present for these reactions. To determine the overall rate constant for Reaction (5.1), the value of the rate constant for Reaction (5.1) in the n-butanol/TBHP mechanism was varied until the simulated OH time-history best fit the measured OH time-history for each temperature data point, similar to the analysis described in Chapter 4. In the analysis of data for n-butanol, the branching ratios for the different abstraction sites of Reaction (5.1) can influence the rate constant determination because certain channel of the reaction can lead to subsequent OH production; branching ratios were not important in the rate constant determination for the reactions of OH with n-alkanes in Chapter 4 because no OH-producing reactions were possible. In the current analysis for the n-butanol data, the site-specific rate constants for Reactions (5.1a) through (5.1e) used in the n-butanol/TBHP mechanism during the analysis were calculated with the temperature-dependent branching ratios from the Zhou et al. [88] work with the G3 potential energy surface. Figure 5.3 illustrates these branching ratios at 1197 K. In this study, the branching ratios were assumed to be constant within the variations of the rate constant for Reaction (5.1).

5.3 Experimental

The shock tube and laser diagnostics described in Chapter 2 of this thesis were used for the work in this chapter. In addition to the chemicals described in Chapter 2 (TBHP/water solution 70%, by weight TBHP, and argon gas), anhydrous n-butanol (99.8% purity) from Sigma Aldrich, was also used in the mixture preparation for the experiments in this chapter. The current experimental procedure closely follows the procedure used by Vasu et al. [47], with added improvements in that the n-butanol composition of the test mixtures was veriﬁed to within ±5% by laser absorption at 5.4. RESULTS 81

3.39 µm in an external multi-pass absorption cell, and the impurities in the shock tube were experimentally conﬁrmed to contribute less than 1 ppm OH using the laser absorption method described in Chapter 2. Measurements of OH time-histories were carried out in shock tube experiments performed with dilute mixture of tert-butylhydroperoxide (TBHP) and n-butanol, with initial n-butanol-to-TBHP concentration ratios of 12 and 20 (150 ppm n-butanol with 13 ppm TBHP, and 201 ppm n-butanol with 10 ppm TBHP, both dilute in argon). Temperatures in the range of 896 to 1197 K were studied; the upper limit of the temperature range was constrained by decomposition of n-butanol and the lower temperature limit was set by slow decomposition of TBHP. Pressures of nominally 1 atm were used, with the exception of a single measurement at 2 atm to compare the results with Vasu et al. [47] under identical experimental conditions.

5.4 Results

The measured OH time-histories typically follow a near-exponential decay after the peak OH concentration is reached. Sample measurement traces of the OH time-history are shown in Figure 5.4 at 1197 K and at 925 K. The simulated OH time-histories with the best-fit rate constant for Reaction (5.1) in the n-butanol/TBHP mechanism are also shown in comparison to the measured traces in Figure 5.4. The effects of perturbations of ±30% on the rate constant for Reaction (5.1) are also shown, illustrating the sensitivity of the simulated OH rate of decay to the rate constant for Reaction (5.1). At temperatures below 1000 K, the decomposition of TBHP occurs over a finite time-scale, as shown in the example measured OH time-history in Figure 5.4 at 925 K where the peak OH mole fraction is not reached until approximately 13 µs. At these temperatures, the OH time-history is accurately modeled by the n-butanol/TBHP mechanism at early times, and only the post-peak-OH behavior shows sensitivity to the rate constant for Reaction (5.1). Therefore, the rate constant for Reaction (5.1) can be determined from measured OH time-histories even at temperatures at which TBHP does not decompose instantaneously. 82 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

Current data 1 k (best fit) 5.1 k + 30% 1197 K, 0.96 atm 5.1 150 ppm n-butanol, k - 30% 10 5.1 13.3 ppm TBHP Reaction (5.1): CH CH CH CH OH + OH 3 2 2 2 -> Products

OH mole fraction [ppm] 925 K, 1.22 atm 201 ppm n-butanol, 10.3 ppm TBHP 1 0 1020304050607080 Time [s]

Figure 5.4: Measured OH time-histories for 1197 K and 0.96 atm for a mixture of 150 ppm n- butanol and 13.3 ppm TBHP, and 925 K and 1.22 atm for a mixture of 201 ppm n-butanol and 10.3 ppm TBHP, shown with simulations with the n-butanol/TBHP mechanism using the best-ﬁt rate constant for Reaction (5.1) and perturbations of ±30%.

The overall rate constant for Reaction (5.1) was determined with the n- butanol/TBHP mechanism for each measured OH time-history. Table 5.1 presents the site-speciﬁc rate constants for Reactions (5.1a) to (5.1e) (calculated using the temperature-dependent branching ratios from the Zhou et al. [88] calculations using the G3 potential energy surface) that were used in the analysis. The measured rate constant was found to be independent of both pressure and initial mixture composition, and the results can be summarized in Arrhenius form by Eq. 5.2 in the temperature range 896 to 1197 K.

! 2505 k = 3.24 × 10−10 exp − cm3molecule−1s−1 (Eq. 5.2) 5.1 T [K]

A list of all experimental conditions for the work in this chapter and the ﬁnal rate constant determined for each individual data point is provided in Table 5.2. The individual data points will be shown on an Arrhenius plot in comparison to other 5.5. INFLUENCE OF SECONDARY REACTIONS 83

works in Section 5.7.

Table 5.2: Determinations of the rate constant for Reaction (5.1) from the experimental OH time- history data.

3 −1 −1 Mixture T [K] P [atm] k5.1 [cm molecule s ] 150 ppm n-butanol, 1028 1.14 2.82 × 10−11 ∼13 ppm TBHP 1095 1.05 3.32 × 10−11 1182 2.04 3.99 × 10−11 1197 0.96 3.99 × 10−11 201 ppm n-butanol, 896 1.24 1.99 × 10−11 ∼10 ppm TBHP 925 1.22 2.16 × 10−11 963 1.17 2.41 × 10−11 993 1.16 2.57 × 10−11 1137 1.00 3.49 × 10−11 1196 0.94 3.99 × 10−11

5.5 Inﬂuence of Secondary Reactions

5.5.1 OH Sensitivity Analysis

Under the experimental conditions studied, Reaction (5.1) dominates the OH sensitivity, deﬁned by Eq. 3.1. Figure 5.5 shows the top six reactions appearing in the OH sensitivity calculated using the n-butanol/TBHP mechanism for representative experimental conditions at 925 K. The OH sensitivity to the individual channels of Reaction (5.1) is shown, along with the overall OH sensitivity to Reaction (5.1), which is computed as the sum of OH sensitivity to the individual channels. The top four reactions contributing to secondary OH sensitivity interference are Reactions (3.1), (3.3), (5.6a), and (5.6b). The OH sensitivity to Reaction (3.1), the unimolecular decomposition of TBHP, is high only at early times, and the rate constant for Reaction (3.1) has been measured in Chapter 3 resulting in accurate simulation of the early-time OH time-history as seen in Figure 5.4. The rate constant for Reaction (3.3) was also measured in Chapter 3, and is assumed to accurately 84 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

describe the secondary reaction of OH with methyl radicals (a ﬁnal decomposition product of TBHP) because the measured values of the rate constant for Reaction (5.1) are independent of initial n-butanol-to-TBHP concentration ratio. Reactions (5.6a) and (5.6b), which also appear in the OH sensitivity analysis, are competing reactions pathways for consumption of the δ-radical; the OH time-history is sensitive only to

the branching ratio k5.6a/k5.6, where k5.6 = k5.6a + k5.6b, because the products of Reaction (5.6a) lead to an OH-producing pathway through Reaction (5.13), while the Reaction (5.6b) is a non-OH-producing reaction channel (Reaction (5.3b) also contributes to consumption and production of the δ-radical, however, its inﬂuence on the δ-radical concentration is negligible in comparison to Reactions (5.6a) and (5.6b)).

(5.1) CH CH CH CH OH + OH -> Products 3 2 2 2 (5.1a) CH CH CH CH OH + OH -> CH CH CH CHOH + H O 3 2 2 2 3 2 2 2 (5.1c) CH CH CH CH OH + OH -> CH CHCH CH OH + H O 3 2 2 2 3 2 2 2 (3.1) (CH ) COOH -> (CH ) CO + OH 1.0 3 3 3 3 (5.6a) CH CH CH CH OH -> CH CH OH + C H 2 2 2 2 2 2 2 4 (5.6b) CH CH CH CH OH -> CH CH CH CH O (3.1) 2 2 2 2 3 2 2 2 0.5 (3.3) CH + OH -> CH (s) + H O 3 2 2 (5.6a) 0.0 (5.6b) (3.3) -0.5

(5.1c)

-1.0 OH Sensitivity (5.1a)

-1.5 925 K, 1.22 atm (5.1) 201 ppm n-butanol, 10.3 ppm TBHP -2.0 0 1020304050607080 Time [s]

Figure 5.5: OH sensitivity calculation with the n-butanol/TBHP mechanism for a mixture of 201 ppm n-butanol and 10.3 ppm TBHP at 925 K at 1.22 atm. The overall rate constant for Reaction (5.1) dominates the OH sensitivity. The four secondary reactions with the highest OH sensitivity are Reactions (3.1), (3.3), (5.6a), and (5.6b).

Minor secondary OH sensitivity interference is also present from Reac- tions (5.2b), (5.2d), (5.4a), and (5.4b), however at a lesser amount than the reactions shown in Figure 5.5. The top reactions appearing in the OH sensitivity analysis are 5.5. INFLUENCE OF SECONDARY REACTIONS 85

The branching ratio k5.1a/k5.1 is greater than k5.1c/k5.1, thus influencing the ordering of the two reactions most significant in the OH sensitivity. The branching ratios k5.1b/k5.1 and k5.1e/k5.1 are assumed to be 6% and 1%, respectively, at 925 K, and therefore these reactions do not contribute significantly to the OH sensitivity. Furthermore, the net OH consumption through Reaction (5.1b) is expected to be near zero because the β-radical product is expected to undergo a rapid beta-scission decomposition to reproduce OH via Reaction (5.4a), and this reaction pathway also contributes to the low OH sensitivity to Reaction (5.1b). The explanation for the near-zero OH sensitivity to Reaction (5.1d) is more complicated, and can be elucidated with the rate of production analysis discussed in the following section.

5.5.2 Reaction Pathway Analysis

Figure 5.6 presents a detailed reaction pathway analysis of the OH radical at 1197 K, and illustrates how secondary reactions can contribute to consumption and production of OH radicals. The net OH rate of production, deﬁned as d[OH]/dt, is also shown compared with the OH rate of production due to Reaction (5.1) and secondary reactions. The secondary reactions that produce OH radicals are Reactions (5.4a) and (5.13), which subsequently occur after formation of the β-radical and δ-radical, respectively. In these reactions, cleavage of the C—OH bond in the radical fragment of n-butanol occurs to produce an OH radical indistinguishable from the OH produced from TBHP, thus retarding the net rate of OH decay. As mentioned in the previous section, the decomposition of the β-radical via Reaction (5.4a) contributes to the near-zero OH sensitivity to Reaction (5.1b). Because Reaction (5.4b) is a non-OH-producing competing pathway for consumption of the β-radical, minor OH sensitivity is present from Reactions (5.4a) and (5.4b). The amount of OH produced 86 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

via Reaction (5.13) is controlled by the branching ratio of k5.6a/k5.6, and therefore only Reactions (5.6a) and (5.6b) appear in the OH sensitivity while the OH sensitivity to Reaction (5.13) is near zero.

Figure 5.6: OH reaction path analysis at 1197 K and 0.96 atm for a mixture of 150 ppm n-butanol and 13.3 ppm TBHP. The net rate of OH consumption (i.e. the observed pseudo-ﬁrst-order rate) is 20% slower than the rate of OH consumption by Reaction (5.1) at these conditions. All values represent calculations at 10 µs.

Using the best-known rate constants listed in Table 5.1 to describe the important n-butanol secondary reactions in the n-butanol/TBHP mechanism, the branching ratio of k5.6a/k5.6 is predicted to be 92% at 1197 K; thus the subsequent reactions to follow Reaction (5.1d) are predicted to mostly lead to OH radical production, causing a near-zero net consumption of OH via Reaction (5.1d), and a negligible OH sensitivity to Reaction (5.1d). Reactions (5.2b) and (5.2d) also lead to production of β-radicals and δ-radicals, and therefore these reactions have a minor contribution to the OH sensitivity. Secondary consumption of OH radicals can also occur, where the dominant secondary reaction for OH consumption is Reaction (3.3), the bimolecular reaction of an OH radical with a methyl radical; this reaction contributes to consumption of OH in any experiment using TBHP as the OH precursor because methyl radicals will be produced at similar levels as OH during TBHP decomposition. The TBHP kinetic 5.5. INFLUENCE OF SECONDARY REACTIONS 87

sub-mechanism was studied in Chapter 3 and accurate rate constants are used in the n-butanol/TBHP mechanism. Therefore, confidence in this mechanism to accurately describe the rate of secondary OH consumption by Reaction (3.3) is high. The rate of production analysis also illustrates that the net OH rate of production (i.e. the pseudo-first-order decay rate) does not quite equal the OH rate of production through Reaction (5.1). For example, the net OH production at 1197 K is 20% slower than the OH rate of production by Reaction (5.1). Thus, directly inferring a rate constant for Reaction (5.1) from the observed pseudo-first-order decay rate can lead to significant errors. Recent results of ab initio calculations presented by Zhang et al. [102] indicate that the rate constant pressure dependence for beta-scission decomposition reactions, such as Reaction (5.3), is stronger than predicted using the Kassel Integral method [99], as is done in the current work. The fall-off factor calculated by Zhang et al. for Reaction (5.3) is approximately an order of magnitude larger than used in the current work, and if similar levels of fall-off exist for similar decomposition processes, such as Reaction (5.6a), this discrepancy can lead to large uncertainties in the predicted branching ratio of k5.6a/k5.6. For example, with the current mechanism this branching ratio is predicted to be 92% at 1197 K; using a rate constant pressure dependence for Reaction (5.6a) that results in a 1-atm rate constant an order of magnitude slower would yield a branching ratio k5.6a/k5.6 that predicts that the Reaction (5.6a) pathway is no longer favored in the consumption of the δ-radical, if all other rate constants remain unchanged. However, Zhang [103] has found that the pressure dependence for the unimolecular isomerization reactions is also expected to be stronger than currently predicted. Therefore, minimal effect of pressure dependence is expected on the branching ratio k5.6a/k5.6 from the difference in estimation methods for pressure dependence, provided that the high-pressure limit rate constants are correct.

As previously mentioned, the branching ratio k5.6a/k5.6 controls the amount of OH reproduction that occurs via Reaction (5.13) and can aﬀect the OH sensitivity to Reaction (5.1d). The detailed uncertainty analysis carried out in the following section shows that the eﬀect of the uncertainty of the branching ratio of k5.6a/k5.6 on the rate constant determination of Reaction (5.1) is the largest contribution to the 88 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

overall uncertainty near 1200 K. An uncertainty factor of 2 has been assumed for the rate constants for the unimolecular reactions in the fall-oﬀ region. Because of the

possibility of signiﬁcant uncertainty in the branching ratio k5.6a/k5.6, further experimental investigations of the pressure-dependent rate constants for Reactions (5.6a) and (5.6b) are recommended.

5.6 Uncertainty Estimation

A detailed uncertainty analysis, accounting for both experimental and rate constant uncertainties was carried out. The major experimental uncertainties are the initial n-butanol concentration in the reactant mixture and the fitting of the data trace, and the major kinetic rate constant uncertainties include the rate constants for Re- actions (3.1), (3.3), (5.2b), (5.2d), (5.4a), (5.4b), (5.6a), and (5.6b). A conservative uncertainty of ±30% each is assumed for the rate constant for Reaction (3.1) and (3.3) (see Chapter 3), and a factor of 2 uncertainty is assumed for each of the rate constants for Reactions (5.2b), (5.2d), (5.4a), (5.4b), (5.6a), and (5.6b). The branching ratios k5.1b/k5.1 and k5.1d/k5.1 also contribute to the uncertainty in the current rate constant determination, and the uncertainty limits for these branching ratios are estimated to be ±30%. To assess individual uncertainties, each independent source of uncertainty was perturbed to its uncertainty limit, and the experimental data trace was refit with a new rate constant for Reaction (5.1). Because not all of the uncertainty factors are independent, the individual uncertainties cannot simply be combined using a root- sum-squares method to obtain an overall uncertainty. For example, the uncertainty in the rate constants for Reactions (5.6a) and (5.6b) are coupled together, as well as with the uncertainty of the branching ratio k5.1d/k5.1. To determine the uncertainty influence of a group of coupled uncertainty factors, each uncertainty source in the group was perturbed to its uncertainty limit (with the directions chosen such that the effects would not cancel out), and the data trace was refit to obtain the uncertainty- influenced determination of the rate constant for Reaction (5.1). A total uncertainty in the rate constant for Reaction (5.1) was determined by combining the effects of 5.7. COMPARISON WITH LITERATURE 89

the coupled uncertainties with the independent individual uncertainties in a root- sum-squares summation. The total estimated uncertainty for the rate constant for Reaction (5.1) is ±20% at 1197 K, where the majority of this uncertainty is due to uncertainties in k5.1d/k5.1, and the rate constants for Reactions (5.6a) and (5.6b). At 925 K, this group of coupled uncertainty factors contributes a smaller amount to the overall uncertainty, however the rate constant for Reaction (3.1) has an important role in the OH sensitivity calculations at these temperatures, leading to an overall uncertainty in the rate constant for Reaction (5.1) at 925 K of approximately ±23%. At this temperature, the largest contribution to the uncertainty becomes the rate constant for Reaction (3.1). Table 5.3 provides details of the eﬀect of the uncertainties on the ﬁnal rate constant determinations at 1197 K and 925 K.

Table 5.3: Individual and coupled uncertainties and inﬂuence of the uncertainties on the determination of the rate constant for Reaction (5.1) at 1197 K and 925 K.

Uncertainty Sources (Uncertainty ascribed to source) Uncertainty in Uncertainty in k5.1 at 1197 K k5.1 at 925 K Experimental Uncertainties Initial n-butanol concentration (±5%) ±5% ±5% Fitting (±10%) ±10% ±10% Modeling Uncertainties

k3.3 (±30%) ±3% ±2% k5.1b/k5.1 (±30%) & k5.4a (factor 2) & k5.4b (factor 2) ±6% ±4% k5.1d/k5.1 (±30%) & k5.6a (factor 2) & k5.6b (factor 2) ±14% ±12% k5.2b (factor 2) ±3% ±2% k5.2d (factor 2) ±4% ±2% k3.1 (±30%) ±0% ±15% Overall RSS Uncertainty ±20% ±23%

5.7 Comparison with Literature

5.7.1 Previous Experiments at High Temperatures

Vasu et al. [47] published the ﬁrst high-temperature measurements of the rate constant for Reaction (5.1) from 1017 to 1269 K. Their experiments employed similar 90 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

techniques as the current work, using narrow-linewidth laser absorption by OH in a shock tube and TBHP as the OH precursor. The current set of experiments includes one measurement at similar temperature, pressure, and mixture composition (1182 K, 2.04 atm, 150 ppm n-butanol, 13 ppm TBHP) as used in the Vasu et al. work (1165 K, ∼2.25 atm, 147 ppm n-butanol, 11 ppm TBHP). This measured OH time-history of the current work is shown in Figure 5.7 in comparison to the closely equivalent trace of Vasu et al. The measured OH time-history of the current work displays a ﬁrst-order decay rate which is closely equal to that which was measured by Vasu et al., indicating that the current measured OH time-history data are in excellent agreement with their work.

Dashed lines show the same rates of first-order decay in the first 30 s 10

Current work 1182 K, 2.04 atm Vasu et al. 150 ppm n-butanol, 1165 K, 2.08 atm 13.5 ppm TBHP 147 ppm n-butanol,

OH mole fraction [ppm] 10.8 ppm TBHP

1 0 102030405060 Time [s]

Figure 5.7: Measured OH time-histories from the current work with conditions 1182 K, 2.04 atm, 150 ppm n-butanol, 13 ppm TBHP and from Vasu et al. [47] with conditions 1165 K, 2.25 atm, 147 ppm n-butanol, 11 ppm TBHP. The data traces show similar measured ﬁrst-order decay rates.

Vasu et al. [47] determined an overall rate constant for Reaction (5.1) using a detailed mechanism which they constructed using an early n-butanol mechanism of Sarathy et al. [32], modiﬁed with TBHP chemistry from literature sources [67, 104]. While Vasu et al. pioneered the high-temperature experimental work on the reaction of OH with n-butanol, recent improved understanding of high-temperature n-butanol 5.7. COMPARISON WITH LITERATURE 91

oxidation kinetics allows for more accurate selection of rate constants for secondary reaction pathways in the current work, as discussed in Section 5.2. Three major diﬀerences exist between the mechanism used in the current analysis and the mechanism constructed by Vasu et al. [47] from the Sarathy et al. [32] mechanism.

1. The mechanism of Sarathy et al. uses a rate constant for Reaction (3.3) that is an order of magnitude slower than the rate constant measured in Chapter 3 of this thesis for the same reaction. The mechanism constructed by Vasu et al., therefore, does not correctly predict secondary OH consumption and under- predicts the rate of OH decay due to TBHP kinetics; this introduces a 7% error in their determination of the rate constant for Reaction (5.1). The uncertainty in the rate constant for Reaction (3.3) was not included in the uncertainty analysis of Vasu et al.

2. The analysis of Vasu et al. assumes the rate constant for Reaction (5.1b) is equal to that in the Sarathy et al. mechanism. This estimation of the rate constant for Reaction (5.1b) is approximately three times faster than the rate constant inferred in the current analysis. The uncertainty in the rate constant for Reaction (5.1b) was accounted for in the uncertainty analysis of Vasu et al.

3. In the analysis by Vasu et al., nearly all (>98% at 1017 K) of the δ-radicals formed were predicted to be consumed through isomerization reactions, instead of unimolecular decomposition which leads to OH production via Re- action (5.13). The rate constants used for Reactions (5.6a) and (5.6b) in the current work suggest that the unimolecular decomposition pathway is favored. Uncertainties for the rate constants Reactions (5.6a) and (5.6b) were not included in the uncertainty analysis of Vasu et al.

The major differences between the current mechanism and the mechanism used in the Vasu et al. analysis are presented in Table 5.4, along with the influence of each of the mechanism differences on the rate constant for Reaction (5.1). The overall influence of all of the mechanism differences is also presented in Table 5.4. 92 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

Table 5.4: Diﬀerences in the mechanisms used for analysis of measured OH time-histories in the current work and the work of Vasu et al. [47], and the inﬂuence on the Vasu et al. determination of the rate constant for Reaction (5.1) at 1165 K.

Rate constant(s) changed Justification Influence on Influence on in current mechanism k5.1 at 1269 K k5.1 at 1017 K

k3.3 (×20) Chapter 3 -7% -7% k5.1b (×0.33) [88] -15% -16% k5.6a & k5.6b (see text) [93, 94, 99] +33% +17% Overall inﬂuence of current mechanism changes +10% -6%

Reaction (5.1): CH CH CH CH OH -> Products 3 2 2 2 1428 K 1250 K 1111 K 1000 K 909 K 833 K 5 ] -1 s

-1 4

3 molecule 3

cm 2

-11 Current work Vasu et al. data as published [10

5.1 Vasu et al. data with current analysis k Zhou et al. calculation CCSD(T) PES Zhou et al. calculation G3 PES 1 0.7 0.8 0.9 1.0 1.1 1.2 1000/T [K-1]

Figure 5.8: Arrhenius plot of the rate constant for Reaction (5.1) determined in the current work (filled squares) compared with rate constant determination as reported in Vasu et al. [47] (open diamonds) and their data reinterpreted with the mechanism from the current work (open squares). Also shown are rate constant calculations from Zhou et al. [88]. The solid line is an Arrhenius fit to the current experimental data, and the dashed line is a fit to the reinterpreted data of Vasu et al. using the current mechanism. The error bars on the current data represent the results of a detailed uncertainty analysis, see Table 5.3. 5.7. COMPARISON WITH LITERATURE 93

Figure 5.8 compares the overall rate constant for Reaction (5.1) determined in the current work with the values determined by Vasu et al. [47] using their reported mechanism. Also shown are the results of a rate constant determination analysis for two raw data traces from the work of Vasu et al. (their highest and lowest temperature data points) using the n-butanol/TBHP mechanism developed for the current work. The figure illustrates that the rate constant as reported in the work of Vasu et al. is within 10% of the current work, with the discrepancy almost entirely due to mechanistic differences in the analysis. This is expected considering, as initially mentioned, that the raw data of OH decay in the current work was found to be in excellent agreement with their work. The current experiments extend the temperature range of the Vasu et al. [47] work, providing the first rate constant measurements for reaction of OH with n- butanol from 900 to 1000 K. The current determination of the rate constant for Reaction (5.1) shows a slightly stronger temperature dependence than was found by Vasu et al., and this temperature dependence is verified over a wider temperature range.

5.7.2 Ab initio Calculations

Zhou et al. [88] performed detailed ab initio calculations for the rate constants for Reaction (5.1a), (5.1b), (5.1c), (5.1d), and (5.1e) using a two-transition-state model. They produced two different potential energy surfaces, using CCSD(T) and G3 methods, yielding two sets of rate constant calculations. Their site-specific rate constant calculations can be summed to obtain the overall rate constant for Reaction (5.1), and these calculated values are compared to the current experimental measurements in Figure 5.8. Their overall rate constant for Reaction (5.1) calculated with the two different methods differ by up to 50% in the temperature range of interest, and the current measurements of the rate constant for Reaction (5.1) fall between the two rate constant calculations. Their calculation using the G3 potential energy surface falls within the uncertainty estimate of the measured value at 1197 K. At 925 K, however, both the G3- and CCSD(T)-calculated value of the rate constant for Reaction (5.1) 94 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

from Zhou et al. fall just outside of the uncertainty limits of the measured rate constant. The temperature dependence of the CCSD(T)-calculated overall rate constant is more representative of the measured rate constant than the G3-calculated value.

5.7.3 Atmospheric-relevant Temperature Rate Constants

Several experimental studies of the rate constant for Reaction (5.1) have been carried out at atmospheric-relevant temperatures from 292 to 372 K. [105–111] A 3-parameter modified Arrhenius expression can be empirically fit to these data and the current determination of the rate constant for Reaction (5.1) at combustion-relevant temperatures for interpolation of the rate constant at intermediate temperatures; Eq. 5.3 presents an expression for the rate constant for Reaction (5.1) that fits experimental data from 372 to 1197 K. ! 1160 1.78 × 10−21T 3.22 exp + cm3molecule−1s−1 (Eq. 5.3) T [K]

Figure 5.9 presents the current recommendation for the rate constant for Reac- tion (5.1) in comparison to the measured rate constants at atmospheric-relevant conditions. The empirical structure-activity relationship (SAR) of Atkinson and coworkers [20–22] introduced in Chapter 4 (and also described in detail in Appendix D) can also be applied to reactions of OH with alcohols, and updated substituent factors for reactions involving alcohols are presented by Bethel et al. [90]. The SAR was developed from rate constant data at atmospheric-relevant temperatures, and adequately represents all data for the rate constant for Reaction (5.1) at both atmospheric- and combustion-relevant temperatures. However, the results of ab initio calculations by Zhou et al. [88] suggest formation of a hydrogen-bonded complex in several of the channels of Reaction (5.1), and therefore the rate constant estimated using the SAR method may not correctly represent the relative rate constants of the overall reaction. The rate constant estimated using the SAR method of Atkinson and coworkers is also shown in Figure 5.9 (labeled Bethel et al. [90]) in comparison to experimental data. 5.8. CONCLUSIONS 95

Reaction (5.1): CH CH CH CH OH -> Products 3 2 2 2 1000 K 500 K 333 K 250 K 5 Experimental Data

] 4

-1 Current work s

-1 Campbell et al. (1976) 3 Wallington and Kurylo (1987) Nelson et al. (1990) 2 Yujing and Mellouki (2001)

molecule Cavalli et al. (2002) 3

Hurley et al. (2009) cm -11 1 Rate Constant [10 Recommendations 5.1 k Current work Bethel et al. (2001)

1.0 1.5 2.0 2.5 3.0 3.5 4.0 1000/T [K-1]

Figure 5.9: Arrhenius plot of the rate constant for Reaction (5.1) determined in the current work shown with published data at atmospheric-relevant conditions. [105–111] Also shown is the 3- parameter ﬁt to the data given by Eq. 5.3 and the overall rate constant estimate from the structure- activity relationship in Bethel et al. [90].

5.8 Conclusions

The rate constant for Reaction (5.1), the overall reaction of OH with n-butanol, was determined from OH time-histories measured behind reflected shock waves, and the results extend the range of experimentally determined high-temperature rate constants to 900 to 1200 K; there were no previous high-temperature measurements below 1017 K. A detailed uncertainty analysis was conducted yielding an overall uncertainty of ±20% at 1197 K and ±23% at 925 K. The largest contributions to the overall uncertainty at 1197 K is the relative rate constant for the channel of Reaction (5.1) that produces a δ-radical, and the rate constants for the reactions leading to consumption of the δ-radical. For decreasing temperatures, the influence of the uncertainty in the rate constant for the OH precursor decomposition reaction also becomes significant. Further experimental investigations on the rate constants important in describing the reproduction pathways of OH from n-butanol are recommended. The measured OH time-histories of the current work are in excellent agreement 96 CHAPTER 5. REACTION OF OH WITH N-BUTANOL

with the similar experiments of Vasu et al. [47]. However, the current determination of the rate constant for Reaction (5.1) disagrees with the Vasu et al. determination for the same reaction by up to 10%, where the discrepancy is almost entirely due to diﬀerences in the kinetic mechanisms used for the analysis. Ab initio rate constant calculations by Zhou et al. [88] using a G3 potential energy surface yield an overall rate constant that shows agreement with the current experimental work at 1197 K, while their rate constant obtained using a CCSD(T) potential energy surface does not. At 925 K, however, both of rate constant calculations by Zhou et al. fall just outside of the uncertainty limits of the measured rate constant. The CCSD(T)-computed overall rate constant of Zhou et al. best matches the temperature dependence of the current data. The empirically developed structure-activity relationship of Atkinson and coworkers [20–22, 90] also agrees within the uncertainty limits of the current rate constant determination. Chapter 6

Reaction of OH with iso-Butanol

6.1 Introduction

6.1.1 Background and Motivation

While the traditional structure of butanol present in biobutanol is the n-butanol isomer, recent technologies have been developed to economically synthesize the iso- butanol isomer (2-methyl-1-propanol) from biomass sources. For example, the strategy developed by Atsumi et al. [112] demonstrates high-yield, high-speciﬁcity production of iso-butanol from glucose using native organisms. Because iso-butanol is becoming an important butanol isomer present in economically-produced biobutanol, developing accurate detailed kinetic mechanisms describing the high-temperature oxidation of iso-butanol is of importance for optimizing the design of practical transportation engines powered by combustion of biobutanol. The hydrogen-atom abstraction by a hydroxyl radical (OH) from iso-butanol is an important elementary reaction in a high-temperature iso-butanol oxidation mechanism because this reaction describes a dominant fuel consumption pathway during the combustion process under many conditions. This reaction can occur via four channels, as described by Reactions (6.1a) through (6.1d), to produce water and a radical with the chemical formula C4H9O in one of the following radical structures: iso-butoxyl or one of four isomers of a hydroxyalkyl radical (α, β, γ, distinguished

97 98 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL

by the radical position with respect to the oxygen atom).1

(CH3)2CHCH2OH + OH −→ (CH3)2CHCHOH + H2O (6.1a)

−→ (CH3)2CCH2OH + H2O (6.1b)

−→ CH3(CH2)CHCH2OH + H2O (6.1c)

−→ (CH3)2CHCH2O + H2O (6.1d)

The radical products are expected to react through rapid isomerization and beta- scission decomposition. Figure 6.1 illustrates the four reaction pathways of Reac- tion (6.1) and the major subsequent reaction pathways. To date, no studies have been found that present experimental data on the rate constant for Reaction (6.1) at combustion-relevant conditions.

iso-Butanol

OH +OH +OH (6.1a) +OH +OH (6.1d) (6.1b) (6.1c)

OH O (α-radical) (iso-butoxyl) OH OH (β-radical) (γ-radical) CH + + 3 (6.2) CH2OH OH + + OH OH

CH3+ H + C3H6 net zero OH (5.12) OH consumption pathway CH O + H OH-consuming reaction 2 OH-producing secondary reaction Other secondary reaction

Figure 6.1: Dominant reaction pathways of iso-butanol after reaction with OH. OH-consuming reactions are shown with red arrows, and OH-producing reactions are shown with green arrows.

1Note that the terms α-radical, β-radical, and γ-radical are also used in Chapter 5 of this thesis to refer to diﬀerent radicals. In this chapter, the Greek letter distinguishes the position of the radical with respect to the hydroxyl group on the radical produced by hydrogen-abstraction from iso-butanol. 6.1. INTRODUCTION 99

6.1.2 Objectives of the Current Chapter

The experimental techniques used in Chapter 4 of this thesis have become a method that is commonly used for measuring OH time-histories to determine rate constants for reactions of OH with combustion-relevant organic compounds. However, the work presented in Chapter 5 elucidated the importance of accounting for subsequent OH- producing reactions in the study of reactions in the family of butanol + OH. For the reaction of OH with iso-butanol, the only critical secondary OH-producing reaction is Reaction (6.2), the beta-scission decomposition of the β-radical (1-hydroxy-2-methyl- prop-2-yl: (CH3)2CCH2OH).

(CH3)2CCH2OH −→ (CH3)2C−CH2 + OH (6.2)

Reaction (6.2) has no significant competing secondary reaction pathways because there is only one C–C bond two bonds away from the radical (hence only one dominant beta-scission pathway) and no isomerization reactions of the radical can occur through 5- or 6-ring transition-state structures (isomerization reactions with larger ring transition states are more likely to occur). Thus, Reaction (6.1b) has a net-zero contribution to the OH consumption, and cannot be measured using the technique described in Chapter 4. The measured data, however, are sensitive to the overall rate constant of all other channels of Reaction (6.1). The site-specific rate constants for Reaction (6.1) can be categorized into three different rate constants, defined by Eq. 6.1, Eq. 6.2, and Eq. 6.3, each of which will be examined in this chapter.

β k6.1 = k6.1b (Eq. 6.1) non-β k6.1 = k6.1a + k6.1c + k6.1d (Eq. 6.2) overall k6.1 = k6.1a + k6.1b + k6.1c + k6.1d (Eq. 6.3)

This chapter presents the results of OH mole-fraction time-history measurements in reﬂected shock experiments of TBHP with iso-butanol in excess and uses the data non-β overall to examine k6.1 and k6.1 . The overall rate constant for Reaction (6.1) minus non-β the rate constant for the β-radical-producing channel, k6.1 , is determined under 100 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL

combustion-relevant conditions from the measured OH mole-fraction time-histories. overall An overall rate constant for Reaction (6.1), k6.1 , is suggested based on the rate con- β stant for the β-radical-producing reaction channel, k6.1, of Merchant and Green [113]. Comparisons to rate constants for Reaction (6.1) presented in the literature are made.

6.2 Experimental

The shock tube and laser diagnostics described in Chapter 2 of this thesis were used for the work in this chapter. In addition to the chemicals described in Chapter 2 (TBHP/water solution 70%, by weight TBHP, and argon gas), anhydrous 99.5% 2- methyl-1-propanol (iso-butanol) from Sigma Aldrich, was used in the mixture preparation for the experiments in this chapter. OH time-histories were measured in reﬂected-shock experiments of mixtures of TBHP with iso-butanol in excess, diluted in argon. Two test mixtures were prepared, 150 ppm iso-butanol with 15 ppm TBHP, and 220 ppm iso-butanol with 15 ppm TBHP, leading to initial iso-butanol-to-TBHP concentration ratios of 10 and 15, respectively. The reﬂected shock conditions were nominally 1 atm, with temperatures ranging from 907 to 1147 K.

6.3 Kinetic Modeling and Analysis

6.3.1 Model Description

A kinetic mechanism was constructed to describe the time evolution of the reaction process with the current test mixtures of dilute TBHP and iso-butanol in excess. In addition to Reactions (6.1a) through (6.1d), this mechanism consists of a base mechanism that includes secondary reactions due to the presence of TBHP as the OH precursor, as well as reactions important in iso-butanol kinetics. The base mechanism used is the n-butanol/TBHP mechanism described in Chapter 5, which contains alkane reactions from the JetSurF 1.0 mechanism [18], reactions and rate constants for the TBHP-related reactions from Chapter 3, and updated rate constants for small alkyl and hydroxyalkyl radical reactions relevant to butanol chemistry. 6.3. KINETIC MODELING AND ANALYSIS 101

The reactions important in iso-butanol kinetics include the subsequent reactions that are expected to occur following Reaction (6.1), as illustrated in Figure 6.1, and Reactions (6.3a) through (6.3d) which describes reactions of hydrogen radicals with iso-butanol, of which can lead to the production of β-radicals.

(CH3)2CHCH2OH + H −→ (CH3)2CHCHOH + H2 (6.3a)

−→ (CH3)2CCH2OH + H2 (6.3b)

−→ CH3(CH2)CHCH2OH + H2 (6.3c)

−→ (CH3)2CHCH2O + H2 (6.3d)

The rate constants describing important secondary reactions of iso-butanol are taken from Merchant and Green [113] and Sarathy et al. [91], and are listed in Table 6.1. The isomerization and beta-scission reactions shown in 6.1 involving the iso-butoxyl and iso-C4H8OH radicals were considered in the current analysis; the following section will demonstrate that the OH time-history is insensitive to rate constants for these reactions, as long as a reasonable estimate was used (k ≥ 105 s−1). In addition to the beta-scission reactions cleaving at the C–C or C–O bonds, beta- scission reactions eliminating a hydrogen radical are also possible; however, these reactions are expected to occur at a much slower rate than the beta-scission reactions that break a C–C or C–O bond, due to bond energy arguments. The relative rate constants for the hydrogen-eliminating beta-scission reactions in the Sarathy et al. mechanism [91] further conﬁrm that the beta-scission reactions breaking a C–H bond are negligible. Therefore, hydrogen-eliminating beta-scission reactions are not included in the current mechanism; however, the inﬂuence of up to 10% of the β- radical reacting through such a channel (instead of regenerating OH) is considered in the uncertainty analysis of the rate constant determination in Section 6.4. Reactions describing the unimolecular decomposition of iso-butanol also were not included in the current mechanism because these reactions are not expected to be important at temperatures less than 1200 K. The addition of the unimolecular decomposition reactions of iso-butanol and the corresponding rate constants (and perturbations of those rate constants by up to a factor of 2) from the Sarathy et al. 102 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL

mechanism [91] to the current mechanism was examined, and these changes introduced negligible change (less than a 2% change in the rate of OH decay) in the simulated OH time-histories at 1200 K. Furthermore, the absence of iso-butanol decomposition was veriﬁed experimentally by using the OH absorption diagnostic in shock-heated mixtures of dilute iso-butanol in argon (without TBHP); no OH formation was observed in these experiments, further supporting the assumption on the absence of iso-butanol decomposition in the current experimental temperature range. The current kinetic mechanism thus contains all the reactions expected to occur under the experimental conditions of the current work; however, this mechanism will not fully describe experiments outside of the current temperature range or iso-butanol oxidation.

Table 6.1: Rate constants for the reactions of signiﬁcance in iso-butanol kinetics that were added to the base mechanism from Merchant and Green [113] and Sarathy et al. [91]. The units of A are [cm3molecule−1s−1], and the units of E are [cal mol−1K−1]. The sum of the three absent rate constants is determined in the current work.

No. Reaction k = A · T b exp(−E/RT ) Reference A b E Reactions with OH

(6.1a) (CH3)2CHCH2OH + OH −−→ - - - This Work (CH3)2CHCHOH + H2O −24 3 (6.1b) (CH3)2CHCH2OH + OH −−→ 2.56 × 10 3.70 −4.94 × 10 Merchant and Green [113] (CH3)2CCH2OH + H2O

(6.1c) (CH3)2CHCH2OH + OH −−→ - - - This Work CH3(CH2)CHCH2OH + H2O

(6.1d) (CH3)2CHCH2OH + OH −−→ - - - This Work (CH3)2CHCH2O + H2O

Reactions with H

−19 3 (6.3a) (CH3)2CHCH2OH + H −−→ 1.46 × 10 2.68 +2.92 × 10 Sarathy et al. [91] (CH3)2CHCHOH + H2 −18 3 (6.3b) (CH3)2CHCH2OH + H −−→ 1.08 × 10 2.40 +4.47 × 10 Sarathy et al. [91] (CH3)2CCH2OH + H2 −18 3 (6.3c) (CH3)2CHCH2OH + H −−→ 2.21 × 10 2.54 +6.76 × 10 Sarathy et al. [91] CH3(CH2)CHCH2OH + H2 −21 3 (6.3d) (CH3)2CHCH2OH + H −−→ 1.57 × 10 3.14 +8.70 × 10 Sarathy et al. [91] (CH3)2CHCH2O + H2 6.3. KINETIC MODELING AND ANALYSIS 103

6.3.2 OH Sensitivity Analysis

The results of an OH sensitivity analysis at 1079 K and 1.1 atm with a representative test mixture are shown in Figure 6.2. The OH sensitivity is deﬁned by Eq. 3.1. The non-β OH sensitivity to k6.1 is dominant, and the magnitudes of the OH sensitivity to the individual channels will follow the order of the branching ratio of the channels, which have not been previously studied in this temperature range. The early-time (ﬁrst ∼ 40 non-β µs) total OH sensitivity to k6.1 does not depend on the non-β branching ratios (i.e. non-β non-β non-β k6.1a/k6.1 , k6.1c/k6.1 , k6.1d/k6.1 ), therefore, no assumptions will be made about non-β these branching ratios in this work. While the OH sensitivity to k6.1 is dominant, β the OH sensitivity to k6.1 is zero, regardless of the branching ratio of this channel. This is expected because the β-radical will rapidly decompose to produce an OH radical via Reaction (6.2) and there are no competing non-OH-producing consumption reaction pathways for the consumption of the β-radical. Hence, Reaction (6.1b) results in a net-zero rate of OH concentration change. Therefore, simulated OH time-histories β non-β are insensitive to k6.1, and the simulated rate of OH decay is sensitive to only k6.1 .

(3.1) . . .(CH ) COOH -> (CH ) CO + OH 3 3 3 3 (3.3) . . .CH + OH -> CH (s) + H2O 3 2 1.0 (6.1a,c,d) (CH ) CHCH OH + OH -> non- radicals + H O 3 2 2 2 (6.1b). . .(CH ) CHCH OH + OH -> -radical + H O 3 2 2 2 0.5 (6.3b) .. .(CH ) CHCH OH + H -> -radical + H 3 2 2 2 (3.1) (6.3b) 0.0 (6.1b) (3.3) -0.5

-1.0 OH Sensitivity

1079 K, 1.1 atm -1.5 220 ppm iso-butanol, (6.1a,c,d) 15 ppm TBHP -2.0 0 20406080 Time [s]

Figure 6.2: OH sensitivity calculation using the current kinetic mechanism at 1079 K, 1.1 atm with 220 ppm iso-butanol and 15 ppm TBHP. 104 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL

Minor OH sensitivity to secondary reactions is present from a reaction of iso- butanol with a hydrogen atom, and reactions related to the TBHP as the OH precursor. Reaction (6.3b) will lead to subsequent OH production via decomposition of the β-radical product. While the rate constant for this reaction is not well known, the OH concentration is only sensitive to this reaction at later times (after the hydrogen radical pool has had time to build up), and thus the early-time OH time-history can be assumed to be relatively insensitive to the rate constant for this reaction. Rate constants for the reactions important in the OH sensitivity analysis that are related to TBHP as the OH precursor, such as Reactions (3.1) and (3.3), have been studied in Chapter 3 of this thesis, with uncertainties of ±30%. The rate constants for the isomerization and beta-scission decomposition of the iso-butanol radicals are not significant in the OH sensitivity analysis, and therefore these rate constants have negligible influence on the OH time-history and estimates for the rate constants for these reactions are sufficient.

6.4 Results and Discussion

6.4.1 Rate Constant Measurements for the non-β Pathways

Four sample measured OH time-histories are shown in Figure 6.3 at representative temperatures over the experimental range. The OH time-histories are shown on a semi-logarithmic plot, illustrating a near-exponential decay at all temperatures after the initial TBHP decomposition to OH, which occurs over a finite time at temperatures under 1000 K. The decomposition rate can be captured by the kinetic mechanism described in Section 6.3. The OH time-histories for the two different mixtures can be compared in Figure 6.3, illustrating that for similar temperatures, a faster OH decay rate will be observed in the mixture with a larger initial iso-butanol- to-TBHP concentration ratio; these measurements confirm the expected behavior. non-β For each experimental temperature, k6.1 was determined by matching a simulated OH time-history from the kinetic mechanism with each measured OH time- non-β history, using k6.1 as the free parameter. The OH simulations from the kinetic 6.4. RESULTS AND DISCUSSION 105

1134 K, 1.0 atm 1079 K, 1.1 atm 10 150 ppm iso-butanol 10 220 ppm iso-butanol 15 ppm TBHP 15 ppm TBHP

1 1

0 20406080 0 20406080

1047 K, 1.1 atm 937 K, 1.2 atm 10 150 ppm iso-butanol 10 220 ppm iso-butanol 15 ppm TBHP 15 ppm TBHP

Measured OH

Current data Simulated OH OH mole fraction [ppm] k (best-fit) non- k -30% 1 non- 1 k +30% non- 0 204060800 20406080

Time [s]

Figure 6.3: Sample OH time-history measurements at temperatures of 1134 K, 1079 K, 1047 K, and 937 K. Left figures are mixture of 150 ppm iso-butanol and 15 ppm TBHP, right figures are 220 ppm iso-butanol and 15 ppm TBHP. Also shown are simulated OH time-histories using the current kinetic non-β mechanism with the best-fit rate constant for k6.1 and with the best-fit rate perturbed by ±30%.

mechanism with the best-ﬁt to the data are shown in Figure 6.3, along with the OH non-β simulations with the best-ﬁt value of k6.1 perturbed by ±30% to illustrate the sen- non-β non-β sitivity of the OH decay rate to k6.1 . Table 6.2 lists the values for k6.1 determined from the current measured OH time-histories for each of the experimental tempera- non-β tures, and Figure 6.4 presents an Arrhenius plot of k6.1 . The data can be described in Arrhenius form by the expression in Eq. 6.4.

! 2, 350 knon-β = 1.84 × 10−10 exp − cm3molecule−1s−1 (Eq. 6.4) 6.1 T [K] 106 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL

Eq. 6.4 is valid over the temperature range 907 to 1147 K. These are the ﬁrst experimental rate constants determined that are associated with Reaction (6.1) in this temperature range.

1250 K 1111 K 1000 K 909 K 833 K 4 Current work Oxidation Mechanisms ]

-1 Data Merchant and Green (2012)

s 2-parameter fit Sarathy et al. (2021) -1 3 Grana et al. (2010) Structure-Activity Relationship Atkinson and coworkers molecule 3 2

cm -11 [10 β non- k

1 0.8 0.9 1.0 1.1 1.2 1000/T [K-1]

non-β Figure 6.4: Rate constant measurements for k6.1 . The error bars represent the results of a detailed uncertainty analysis. Also shown are comparisons to the corresponding rate constants used in recently developed iso-butanol oxidation mechanisms [40, 91, 113] and using the structure-activity relationship of Atkinson and coworkers [20–22, 90].

A detailed uncertainty analysis was performed to examine the total uncertainty non-β in the determination of k6.1 based on uncertainties in temperature, pressure, initial TBHP and iso-butanol concentrations, laser intensity and wavelength, OH absorption coefficient, data fitting, impurities, branching ratios of the non-β reactions, the rate constants of the three most important secondary reactions in the mechanism, and the possible influence of unimolecular iso-butanol decomposition reactions and hydrogen-producing beta-scission reactions of the β-radical that were omitted from the mechanism. The influence of these uncertainties on the total uncertainty on non-β k6.1 is estimated to be ±12% at temperatures above 1000 K, with the laser noise and the initial iso-butanol concentration as the dominant factors contributing to the 6.4. RESULTS AND DISCUSSION 107

non-β overall Table 6.2: Rate constants k6.1 and k6.1 for each experimental data point, and the resulting branching ratio for the β-channel. All rate constants are in units of cm3molecule−1s−1.

β non-β β overall k6.1 Mixture T [K] P [atm] k6.1 from data k6.1 from [113] k6.1 overall [%] k6.1 150 ppm iso-butanol, 1147 1.0 2.37 × 10−11 4.68 × 10−12 2.84 × 10−11 16 15 ppm TBHP 1134 1.0 2.31 × 10−11 4.60 × 10−12 2.77 × 10−11 17 1047 1.1 1.96 × 10−11 4.11 × 10−12 2.37 × 10−11 17 1011 1.1 1.74 × 10−11 3.93 × 10−12 2.14 × 10−11 18 220 ppm iso-butanol, 1079 1.1 2.13 × 10−11 4.28 × 10−12 2.55 × 10−11 17 15 ppm TBHP 974 1.2 1.62 × 10−11 3.76 × 10−12 1.99 × 10−11 19 937 1.2 1.49 × 10−11 3.60 × 10−12 1.85 × 10−11 19 925 1.2 1.49 × 10−11 3.55 × 10−12 1.85 × 10−11 19 907 1.2 1.37 × 10−11 3.48 × 10−12 1.72 × 10−11 20 total uncertainty. Uncertainty in the rate constants for the three most important sec- non-β ondary reactions have only a small (<4%) contribution to the uncertainty in k6.1 at temperatures over 1000 K. This was determined using an uncertainty of ±30% for the rate constants for Reactions (3.1) and (3.3), and an uncertainty factor of 2 for the Reaction (6.3b). While the large uncertainty of the rate constant for the latter reaction can have a significant effect on the late-time OH mole fraction (at times >40 µs), there is only minimal effect on the early-time OH decay rate; only the early-time OH decay rate was used for the rate constant determination. For temperatures below 1000 K, the uncertainty of the rate constant for Reaction (3.1) (the TBHP decompo- non-β sition reaction) becomes a more significant factor in the overall uncertainty of k6.1 non-β as the temperature decreases, and the largest overall uncertainty for k6.1 is ±21% at 907 K. These uncertainty limits are illustrated in Figure 6.4.

6.4.2 Comparison to Rate Constant Recommendations

Several detailed kinetic mechanisms for iso-butanol oxidation have been developed in recent years [31, 37, 40, 91, 113]. Each of these mechanisms includes four site- speciﬁc rate constants for Reactions (6.1a), (6.1b), (6.1c), and (6.1d), estimated by examination of the rate constants for analogous reactions. Comparison of the current non-β determination of k6.1 with the corresponding rate constant sum from three most recent mechanisms [40, 91, 113] is shown in Figure 6.4. The rate constant sum from the Merchant and Green mechanism [113] shows the best agreement with the current 108 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL

work. Over the current experimental temperature range, the rate constant sum from the Sarathy et al. mechanism [91] is 15 to 25% slower than the current measurements, and the rate constant sum from the Grana et al. mechanism [40] is 25 to 40% slower than the current measurements. The rate constant sum from the Sarathy et al. and Grana et al. mechanisms show agreement within the uncertainty limits of the current work only at the lowest temperatures studied. Atkinson and coworkers [20–22, 90] developed an empirical structure-activity relationship (SAR) to estimate the rate constants for reactions of OH with organic compounds, including alcohols, at temperatures from 250 to 1000 K. The parameters in their SAR include a rate constant term for each hydrogen-atom abstraction site (primary, secondary, and tertiary carbons and hydroxyl group) in the organic compound, and substituent factors that influence the rate constant term at each reaction site based on the identity of the neighboring substituent groups. Further description of using the SAR method of Atkinson and coworkers to estimate rate constant pa- non-β rameters is presented in Appendix D. An estimation of k6.1 using the updated SAR method can be computed by omitting the rate constant term and substituent factors associated with reaction at the tertiary carbon site of iso-butanol (the reaction site leading to a β-radical product); this computed rate constant is shown in comparison non-β to the current work in Figure 6.4. The estimated k6.1 determined with the SAR method is in very good agreement with the current work. The current results are useful in validating high-level ab initio rate constant calculations for the site-specific channels of Reaction (6.1), such as those by Zheng et non-β al. [114]. Their calculated k6.1 , obtained by the sum of the respective site-specific rate constants calculated using a potential energy surface based on CCSD(T)/CBS, is approximately a factor of 1.5 lower than the current measurements at 1000 K. In the absence of the current experiments, one might believe CCSD(T)/CBS to be more reliable than density functional theory. However, the calculated rate constant using a potential energy surface based on M08-SO/MGS, also done by Zheng et al., is found to have better agreement with the current work than the CCSD(T)/CBS-based rate constant calculations. This observation demonstrates the utility of the current experimental results as a guide for theoretical work. 6.5. OVERALL RATE CONSTANT RECOMMENDATION 109

6.5 Overall Rate Constant Recommendation

The total overall rate constant for Reaction (6.1) can be determined from the current β measurements if an estimate of k6.1 is made. The temperature-dependent expression β for k6.1 found in the Merchant and Green mechanism [113] was chosen to best represent non-β the actual value, for the reasons that their total k6.1 shows excellent agreement with β the current data. The expression for k6.1 in the Merchant and Green mechanism is approximated by using the rate constant for the hydrogen-atom abstraction by OH from the β-carbon site of n-butanol, from the high-level ab initio calculations of Zhou et al. [88], with an adjustment in the activation energy to account for the diﬀerence in the C–H bond energy between a tertiary and secondary carbon; this rate constant is listed in Table 6.1.

β The total overall rate constant is the sum of k6.1 from the Merchant and Green non-β mechanism [113] and the measured k6.1 from the current work, as deﬁned by the expression in Eq. 6.5.

overall non-β β k6.1 = [k6.1 ]meas. + [k6.1]Merchant and Green (Eq. 6.5)

β overall Values for k6.1 and k6.1 at each experimental temperature are listed in Table 6.2. β overall The branching ratio for the β reaction channel, deﬁned as k6.1/k6.1 , is also listed, and over the temperature range studied, 17 to 20% of the overall reaction of OH with iso-butanol is expected to produce a β-radical product under the assumptions used in the current analysis.

overall Figure 6.5 presents k6.1 at each experimental temperature on an Arrhenius overall plot. In the current experimental temperature range of 907 to 1147 K, k6.1 can be expressed in Arrhenius form by Eq. 6.6.

! 2155 koverall = 1.85 × 10−10 exp − cm3molecule−1s−1 (Eq. 6.6) 6.1 T [K]

The current work represents the ﬁrst experimentally-determined rate constant for Reaction (6.1) at combustion-relevant temperatures. 110 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL

1000 K 500 K 333 K 250 K

] 5

-1 Experimental Data Oxidation Mechanisms

s 4 Current work Merchant and Green (2012) -1 Anderson et al (2010) Sarathy et al. (2012) 3 Mellouki et al (2004) Grana et al. (2010) Wu et al. (2003) Structure-activity Relationship Current Recommendation Atkinson and coworkers

molecule 3-parameter fit

3 2 cm

-11

[10 1 overall k

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1000/T [K -1]

Figure 6.5: Overall rate constant for the reaction of OH with iso-butanol from the current work and measurements from the literature [111, 115, 116] at near-atmospheric temperatures and pressures. β overall The error bars represent only the inﬂuence of the k6.1 discrepancies on the uncertainty of k6.1 . Also shown are corresponding rate constants used in published iso-butanol oxidation mechanisms [40, 91, 113], a recommendation from the structure-activity relationship of Atkinson and coworkers [20– 22, 90], and the current recommendation.

The overall rate constant for Reaction (6.1) has previously been studied at at near-atmospheric temperatures and pressures using relative-rate methods by Wu et al. [111], Mellouki et al. [115], and Anderson et al. [116]. Mellouki et al. also used a pulsed laser photolysis-laser-induced ﬂuorescence method for absolute rate measurements. These data are also shown on Figure 6.5. By combining the current rate constant recommendation at high-temperatures with the atmospheric-temperature overall data from the literature, k6.1 can be described with a 3-parameter expression in modiﬁed Arrhenius form by Eq. 6.7, valid from 296 to 1147 K.

! 1304 k = 1.65 × 10−21T 3.18 exp + cm3molecule−1s−1 (Eq. 6.7) overall T [K]

overall The recommended expressions for k6.1 given by Eq. 6.6 and Eq. 6.7 are purely 6.5. OVERALL RATE CONSTANT RECOMMENDATION 111

empirical relations. The uncertainties of the data used in generating the expression overall overall for k6.1 should be taken into account when using these expressions for k6.1 . The low-temperature data exhibit a negative temperature dependence, which can be indicative of initial formation of a hydrogen-bonded complex and, therefore, the rate constant at low temperatures may be pressure and bath gas dependent; thus, caution overall must be taken when applying the current expression for k6.1 at low temperatures (less than 400 K) and pressures (less than 100 Torr).

overall The current recommendation for k6.1 is compared with the corresponding recommendations from the structure-activity relationship (SAR) of Atkinson and coworkers [20–22, 90] and the three mechanisms [40, 91, 113] in Figure 6.5. Ap- pendix D described the process of using the SAR to determine the rate constant. overall The prediction of k6.1 with the SAR method extrapolated to the current temperature range provides a reasonable ﬁt to both the current high-temperature data and the low-temperature measurements [111, 115, 116], and is shown in Figure 6.5. None overall of the mechanism recommendations for k6.1 agree with both the current overall rate constant determinations at high temperatures and the low-temperature data.

β While k6.1 was taken from the Merchant and Green mechanism [113] to determine overall β k6.1 , the values for k6.1 suggested by the Sarathy et al. [91] and Grana et al. [40] β β mechanisms can also be reasonable estimates for k6.1, as they are slower than k6.1 from the Merchant and Green recommendation by less than a factor of two. Further- more, the rate constant term and substituent factors associated with reaction at the tertiary carbon site of iso-butanol from the structure-activity relationship of Atkin- son and coworkers [20–22, 90] (see Appendix D) yields a rate constant representing β k6.1 approximately 1.5 faster than the Merchant and Green recommendation. These β discrepancies in k6.1 contribute an uncertainty of less than ±10% in the total overall β rate constant for Reaction (6.1), as shown in 6.5. The choice of k6.1, given the current literature sources, does not have a significant impact on the current determination of overall overall k6.1 relative to the large discrepancies in the value of k6.1 from each mechanism β and the SAR method. The different expressions for k6.1 from the current literature β overall sources will lead to different branching ratio estimations for k6.1/k6.1 , ranging from β 9% at the lowest using k6.1 from the Sarathy et al. mechanism to 27% at the highest 112 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL

β using k6.1 from the SAR method.

6.6 Conclusions

A rate constant for the non-β-radical producing channels of the reaction of OH with non-β iso-butanol (k6.1 ) was determined from OH time-history measurements in reflected- shock experiments of tert-butylhydroperoxide with iso-butanol in excess. To the best of the author’s knowledge, these are the first experimentally determined rate constants related to the reaction of OH with iso-butanol to be published at combustion- relevant conditions. The site-specific rate constants for the overall reaction of OH with iso-butanol in the most recent Merchant and Green mechanism [113] sum to non-β non-β a k6.1 that matches the current measurements well. The k6.1 predicted from extrapolation of the structure-activity relationship of Atkinson and coworkers [20– 22, 90] to high-temperatures also shows good agreement with the current data. An overall overall rate constant recommendation (k6.1 ) is provided at high-temperature conditions from 907 to 1147 K by using the rate constant from the Merchant and Green mechanism [113] for the β-radical-forming reaction channel, and a three-parameter expression for the overall rate constant is suggested that matches both the current high-temperature rate constant recommendation and low-temperature measurements from the literature [111, 115, 116]. Chapter 7

Reaction of OH with sec-Butanol

7.1 Introduction

7.1.1 Background and Motivation

The sec-butanol isomer of butanol (2-butanol) can be produced from glucose through a process involving fermentation and other chemical processes [117]. Thus, the combustion chemistry of sec-butanol is of interest in kinetic mechanisms describing the combustion of biobutanol. The reaction of OH with sec-butanol can occur through ﬁve diﬀerent reaction channels, described by Reactions (7.1a) through (7.1e).

CH3CH(OH)CH2CH3 + OH −→ CH2CH(OH)CH2CH3 + H2O (7.1a)

−→ CH3C(OH)CH2CH3 + H2O (7.1b)

−→ CH3CH(OH)CHCH3 + H2O (7.1c)

−→ CH3CH(OH)CH2CH2 + H2O (7.1d)

−→ CH3CH(O)CH2CH3 + H2O (7.1e)

Similar to the reactions pathways possible for n-butanol and iso-butanol, as discussed in Chapters 5 and 6, respectively, the C4H9O radicals produced from the hydrogen- atom abstraction reactions will react via beta-scission reactions and isomerization

113 114 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL

reactions. Cleavage at C–C and C–O bonds are the dominant channels for the beta- scission reactions (cleavage at C–H bonds will occur to a lesser extent), and the dominant isomerization reactions are the ones proceeding through a 5-membered-ring transition state. Figure 7.1 illustrates the dominant reactions occurring subsequent to Reaction (7.1).

Reactions (7.2a) and (7.3a) are secondary OH-generating reactions that will occur, and thus the determination of the rate constant for Reaction (7.1) from a measured pseudo-ﬁrst-order OH decay will be complicated by these reactions and any non-OH- producing competing reaction channels, such as Reactions (7.2b), (7.2c), and (7.3b).

CH2CH(OH)CH2CH3 −→ 1− C4H8 + OH (7.2a)

−→ CH2CHOH + C2H5 (7.2b)

−→ CH3(OH)CHCH2CH2 (7.2c)

CH3CH(OH)CHCH3 −→ 2− C4H8 + OH (7.3a)

−→ CH3CH−CHOH + CH3 (7.3b)

Formation of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals that can lead to secondary OH-producing reactions can also occur through hydrogen- abstraction from sec-butanol by hydrogen radicals that are eventually produced from subsequent decomposition of the C4H9O radicals. The hydrogen-abstraction from sec- butanol by hydrogen radicals can occur through ﬁve diﬀerent pathways as described by Reactions (7.4a) through (7.4e).

CH3CH(OH)CH2CH3 + H −→ CH2CH(OH)CH2CH3 + H2 (7.4a)

−→ CH3C(OH)CH2CH3 + H2 (7.4b)

−→ CH3CH(OH)CHCH3 + H2 (7.4c)

−→ CH3CH(OH)CH2CH2 + H2 (7.4d)

−→ CH3CH(O)CH2CH3 + H2 (7.4e) 7.1. INTRODUCTION 115

OH-consuming reaction sec-butanol OH-producing secondary reaction OH Other secondary reaction (7.1a) (7.1e) +OH +OH (7.1b) (7.1d) (7.4a) +H (7.1c) +H +OH +OH (7.4e) +H +OH +H +H (7.4b) (7.4c) (7.4d)

OH OH O OH (7.2c) OH

CH2CH(OH)CH2CH3 CH3CH(OH)CHCH3 (7.3b) (7.2a) (7.2b) (7.3a) O OH OH OH + OH OH OH + + + + + CH3 C2H5 + C2H5 CH3

C2H4OH+H C2H4+H C2H4+H

Figure 7.1: Dominant reaction pathways of sec-butanol after reaction with OH. OH-consuming reactions are shown with red arrows, and OH-producing reactions are shown with green arrows.

Few studies have been found that focus speciﬁcally on the rate constants for Reac- tions (7.2), (7.3), or other secondary reactions occurring subsequent to Reaction (7.1). However, detailed kinetic mechanisms describing global oxidation of sec-butanol have been published by Moss et al. [31], Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91]. These mechanisms contain rate constants for secondary reactions occurring subsequent to Reaction (7.1) and can be used in the analysis of data sensitive to the overall rate constant for Reaction (7.1).

7.1.2 Objectives of the Current Chapter

This chapter presents the results of OH time-history measurements in shock tube experiments of mixtures of tert-butylhydroperoxide (TBHP), as a fast source of OH, with sec-butanol in excess. Three kinetic mechanisms from the literature are used to analyze the OH time-history measurements and an overall rate constant for Reac- tion (7.1) is presented. The sensitivity of the rate constant determination to secondary chemistry is also discussed. 116 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL

7.2 Experimental

The shock tube and laser diagnostics described in Chapter 2 of this thesis were used for the work in this chapter. In addition to the chemicals described in Chapter 2 (TBHP/water solution 70%, by weight TBHP, and argon gas), anhydrous 99.5% sec- butanol (2-butanol) from Sigma Aldrich, was used in the mixture preparation for the experiments in this chapter. OH time-histories were measured in reﬂected-shock experiments of mixtures of TBHP with sec-butanol in excess, diluted in argon. Two test mixtures were prepared, containing 151 ppm sec-butanol with nominally 14 ppm TBHP, and 214 ppm sec-butanol with nominally 14 ppm TBHP. Temperatures of 888 to 1178 K were studied at pressures around 1 atm.

7.3 Secondary Reaction Pathway Modeling

As shown by Figure 7.1, Reactions (7.2a) and (7.3a) are secondary OH-generating reactions that will occur subsequent to Reactions (7.1a) and (7.1c), respectively. Therefore, simulated OH time-histories using a sec-butanol detailed kinetic mechanism are expected to be sensitive to the relative amount of Reaction (7.1) that proceeds via Reactions (7.1a) and (7.1c); this can be described by the branch-

ing ratios k7.1a/k7.1 and k7.1c/k7.1. Furthermore, Reactions (7.2b) and (7.2c) are non-OH-producing reactions competing with Reaction (7.2a) as a decomposition

pathway for the CH2CH(OH)CH2CH3 radical, and Reaction (7.3b) is a non-OH- producing reaction competing with Reaction (7.3a) as a decomposition pathway for

the CH3CH(OH)CHCH3 radical. Thus, simulated OH time-histories are also expected

to be sensitive to the branching ratios k7.2a/k7.2 and k7.3a/k7.3. Knowledge of these branching ratios are necessary to determine the rate constant for Reaction (7.1) from the experimental data collected for this chapter. Detailed kinetic mechanisms describing sec-butanol combustion, such as those by Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91], can be used to account for secondary reaction pathways. Each of these mechanisms can be modiﬁed with the reactions and rate constants presented in Table 3.1 to correctly account for the 7.3. SECONDARY REACTION PATHWAY MODELING 117

OH time-history behavior associated with TBHP; in this text, the use of the term “modified” to describe one of these sec-butanol mechanisms refers to the addition and/or modification of the reactions and rate constants in Table 3.1. Figure 7.2 presents the results of an OH sensitivity analysis of the modified Sarathy et al. mechanism under typical experimental conditions. OH sensitivity is defined by Eq. 3.1. The rate constant for Reaction (7.1) dominates the OH sensitivity; however, Reactions (3.3), (7.3b), and (7.3a), (7.4c), among others, are shown to influence the simulated OH time-history, as would be expected from examination of the reaction pathways in Figure 7.1. The secondary reactions appearing in the OH sensitivity analysis support conclusions suggesting the importance of the branching ratios k7.1a/k7.1, k7.1c/k7.1, k7.2a/k7.2 and k7.3a/k7.3 in the simulated OH time-history. Similar OH sensitivity analysis results are generated with the modified Grana et al. and Van Geem et al. mechanisms.

(3.1) (CH ) COOH -> (CH ) CO + OH 3 3 3 3 (3.3) CH + OH -> CH (s) + H O 1.0 3 2 2 (7.1) CH CH(OH)CH CH + OH -> Products 3 2 3 (7.3a) CH CH(OH)CHCH -> 2-C H + OH 3 3 4 8 (7.3b) CH CH(OH)CHCH -> CH CH =CH OH + CH 0.5 (3.1) 3 3 3 2 2 3 (7.4c) CH CH(OH)CH CH + OH -> CH CH(OH)CHCH + H 3 2 3 3 3 2 (7.3a) 0.0 (7.4c) (7.3b)

(3.3) -0.5 OH Sensitivity

-1.0 969 K, 1.15 atm (7.1) 214 ppm secbutanol, 14 ppm TBHP -1.5 0 20406080100 Time [s]

Figure 7.2: OH sensitivity analysis of the 214 ppm sec-butanol and 14 ppm TBHP mixture at 969 K and 1.15 atm using the Sarathy et al. [91] mechanism.

To the author’s knowledge, no studies have focused directly on any of the branching ratios important in simulating the OH time-history under the current experimental conditions; however, each detailed mechanism contains estimated rate constants for the reactions needed in calculating the branching ratios. Figure 7.3 illustrates the 118 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL

branching ratios k7.1a/k7.1 and k7.1c/k7.1 at 969 K as described by the mechanisms of Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91]. These three mechanisms show reasonable agreement on the branching ratios for k7.1a/k7.1 and k7.1c/k7.1.

The branching ratios k7.2a/k7.2 and k7.3a/k7.3 calculated at 969 K from the three mechanisms are shown in Figure 7.4. The relative amounts of OH regeneration subsequent to the formation of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals do not reach agreed-upon values when comparing the predicted branching ratios from the three mechanisms.

Relative branching in the OH + sec-butanol reaction at 969 K Grana et al. OH

+OH +OH +OH +OH +OH (7.1a) (7.1b) (7.1d) (7.1e) (7.1c) OH OH OH OH O

17% 33% 28% 17% 5% Van Geem et al. OH

+OH +OH +OH +OH +OH

OH OH OH OH O

14% 49% 24% 7% 6%

Sarathy et al. OH

+OH +OH +OH +OH +OH

OH OH OH OH O

17% 44% 17% 18% 4%

Figure 7.3: Branching ratios for Reactions (7.1a) through (7.1e) as suggested by the detailed mechanisms of Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91] The thickness of the arrows illustrate the relative rates of each reaction channel.

Modiﬁed versions of the Grana et al. [40], Van Geem et al. [37], and Sarathy 7.3. SECONDARY REACTION PATHWAY MODELING 119

et al. [91] mechanisms are used for the analysis of the measured OH time-histories reported in this chapter. These three mechanisms will each be used to determine the rate constant for Reaction (7.1) from the experimental data and to explore the sensitivity of the determination of the rate constant for Reaction (7.1) to secondary chemistry. The rate constant for Reaction (7.1) is inferred for each measured data trace using a kinetic mechanism by adjusting the rate constant for Reaction (7.1) in the mechanism to generate a simulated OH time-history that ﬁts the experimental data. In the analyses, the relative branching between Reactions (7.1a) through (7.1e)

(i.e. k7.1a/k7.1, etc.) suggested by each mechanism are preserved, as well as the rate constants for all secondary reactions.

Reaction pathways of +OH +OH Reaction pathways of (7.1a) (7.1c) CH2CH(OH)CH3CH3 CH3CH(OH)CHCH3

OH Grana et al. OH Grana et al.

6% 11% 15% 10% 83% (7.2c), etc. 75% other OH + (7.2a) other OH + (7.3a) (H + enols, (H + enols) (7.3b) (7.2b) gamma-radical, etc.) + CH HO + C2H5 HO 3

OH Van Geem et al. OH Van Geem et al. 82% 77% 9% 0% (7.2c), etc. other 23% other OH + (7.2a) 9% OH + (7.3a) (H + enols, (H + enols) (7.2b) gamma-radical, (7.3b) etc.) + HO C2H5 HO + CH3

OH Sarathy et al. OH Sarathy et al.

15% 0% 53% 4% (7.2c), etc. 85% 43% other OH + (7.2a) OH + (7.3a) other (H + enols, (H + enols) (7.2b) gamma-radical, (7.3b) etc.) + HO + C2H5 HO CH3

Figure 7.4: Branching ratios for the consumption of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals as suggested by the detailed mechanisms of Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91]. The thickness of the arrows illustrate the relative rates of each reaction channel. 120 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL

7.4 OH Time-histories and Rate Constant Deter- mination

A representative measured OH time-history at 969 K is shown in Figure 7.5 with the simulated OH time-history from the modified mechanism of Sarathy et al. [91] with the value of the rate constant for Reaction (7.1) (1.25×10−11 cm3molecule−1s−1) that leads the best fit to the measured trace. Also shown are simulations using perturbations of the best-fit rate constant for Reaction (7.1) by ±30%, illustrating the sensitivity of the simulated OH decay rate to the rate constant. While a rate constant for Reaction (7.1) of 1.25 × 10−11 cm3molecule−1s−1 in the modified Sarathy et al. mechanism leads to a simulated OH time-history that shows an excellent fit to the data at at 969 K, a value of 1.88 × 10−11 cm3molecule−1s−1 for the rate constant for Reaction (7.1) is needed in the modified Van Geem et al. mechanism to generated a simulated OH time-history that matches the experimental data. Thus, the determination of the rate constant for Reaction (7.1) from the experimental data is mechanism dependent, indicating differences in the modeling of secondary reactions.

969 K, 1.15 atm 214 ppm sec-butanol, 14 ppm TBHP 10

Data 1 Simulation, best fit 1 OH mole fraction [ppm] Simulation, k + 30% 7.1 Simulation, k - 30% 7.1 1 0 20406080100 Time [s]

Figure 7.5: Measured OH time-history for an experiment at 969 K, 1.15 atm with 214 ppm sec- butanol and 14 ppm TBHP. Also shown are simulated OH time-histories using the modified mechanism of Sarathy et al. [91] with the best-fit value of the rate constant for Reaction (7.1) and perturbations of ±30% on the best-fit value of the rate constant for Reaction (7.1). 7.4. OH TIME-HISTORIES AND RATE CONSTANT DETERMINATION 121

Figure 7.6 presents an Arrhenius plot of the mechanism-dependent rate constant for Reaction (7.1) determined from the experimental data, and also illustrates the sensitivity of the inferred value of the rate constant for Reaction (7.1) to the kinetic mechanism used for analysis. Table 7.1 presents a list of the inferred rate constants for each experimental data point from all three mechanisms. The peak-to-peak discrepancy of the inferred value of the rate constant for Reaction (7.1) from the different mechanisms is approximately a factor of 0.5, with the rate constant inferred using the modified Grana et al. mechanism the slowest, and the rate constant inferred using the modified Van Geem et al. mechanism the fastest. The analysis using the modified Sarathy et al. mechanism results in rate constant determinations similar to those determined using the modified Grana et al. mechanism.

Reaction (7.1): CH CH(OH)CH CH + OH -> Products 3 2 3 1250 K 1111 K 1000 K 909 K 833 K

] 4

-1 Mechanism: s 3 Grana et al. (2010) -1 Van Geem et al. (2010) Sarathy et al. (2012) 2 molecule 3

cm -11 1 [10 Solid line - Rate constant determination

7.1 from measured data with k different secondary chemistry Dotted line - Rate constant in mechanism 0.6 0.8 0.9 1.0 1.1 1.2 1000/T [K-1]

Figure 7.6: Arrhenius plot of the rate constant for Reaction (7.1) determined using three different modified kinetic mechanisms for sec-butanol from the literature [37, 40, 91]. Points are shown for the rate constant determination for each individual data point using the modified Sarathy et al. mechanism [91], along with a fit to the data points (solid line). For clarity, only the fits to the rate constant determinations using the modified Grana et al. [40] and Van Geem et al. [37] mechanisms are shown. Also shown (dashed lines) are the rate constants in the Grana et al. and Sarathy et al. mechanisms (the rate constant from the Van Geem et al. mechanism does not fit on a reasonable scale on the figure).

The rate constant determination dependence on mechanism is not surpris- ing given that the mechanisms predict diﬀerent branching pathways for the 122 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL

CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals, as illustrated by Figure 7.4. The mechanisms of Grana et al. and Sarathy et al. both ascribe rate constants for the channels of Reactions (7.2) and (7.3) that predict the non-OH-forming decomposition/isomerization reaction channels of the CH2CH(OH)CH2CH3 and

CH3CH(OH)CHCH3 radicals to be dominant. Therefore, the majority of the decay in simulated OH time-histories using the modiﬁed mechanisms of Grana et al. and Sarathy et al. is caused by Reaction (7.1). In the Van Geem et al. mechanism, however, the rate constants for Reactions (7.2) and (7.3) describe reaction pathways indicating that the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals will react dominantly through OH-producing channels. This leads to simulated OH regeneration, and thus a faster value for the rate constant for Reaction (7.1) is needed to simulate the same experimental OH time-history. Reactions (7.2a), (7.2b), (7.2c), (7.3a), and (7.3b) are obviously important secondary reactions in the analysis of the current data. However, to the author’s knowledge, no studies have focused directly on the rate constants for these reactions or the branching ratios of interest. Therefore, the secondary chemistry described by these reactions from the diﬀerent mechanisms will be assumed to represent the approximate bounds of uncertainty in the rate constant determination. The overall rate constant for Reaction (7.1) can be described by the expression in Eq. 7.1 with uncertainty limits of ±30%, valid from 888 to 1178 K.

! 1550 kav. = 6.97 × 10−11 exp − cm3molecule−1s−1 (Eq. 7.1) 7.1 T [K]

av. Eq. 7.1 was determined using a linear least-squares ﬁt to ln(k7.1) versus 1/T , where av. ln(k7.1) at each temperature was taken to be the average of the three ln(k7.1) values determined from each mechanism for each data point. The uncertainty limit of ±30% accounts for the uncertainty in the secondary chemistry within the analysis; this uncertainty is larger than the experimental errors, and thus approximately represents the overall uncertainty of the rate constant for Reaction (7.1), including all experimental and modeling errors. This averaged overall rate constant for Reaction (7.1) is listed in Table 7.1 for each data point and shown in Figure 7.7. 7.5. DISCUSSION 123

Table 7.1: Rate constant determination for Reaction (7.1) for each experimental data point using the modiﬁed mechanisms of Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91]. av. av. Also listed is k7.1 where ln k7.1 was taken to be the average of the three ln k7.1 values determined from each mechanism determination at each temperature point. All rate constants are in units of cm3molecule−1s−1.

av. Mixture T [K] P [atm] k7.1 k7.1 k7.1 k7.1 Grana et al. Van Geem et al. Sarathy et al. 151 ppm sec-butanol, 1112 1.03 1.41 × 10−11 2.24 × 10−11 1.58 × 10−11 1.71 × 10−11 15 ppm TBHP 1032 1.09 1.33 × 10−11 1.99 × 10−11 1.33 × 10−11 1.52 × 10−11 977 1.10 1.28 × 10−11 1.91 × 10−11 1.28 × 10−11 1.46 × 10−11 214 ppm sec-butanol, 1178 0.95 1.58 × 10−11 2.50 × 10−11 1.74 × 10−11 1.90 × 10−11 14 ppm TBHP 1144 0.99 1.54 × 10−11 2.41 × 10−11 1.66 × 10−11 1.83 × 10−11 1118 1.00 1.41 × 10−11 2.24 × 10−11 1.58 × 10−11 1.71 × 10−11 969 1.15 1.25 × 10−11 1.88 × 10−11 1.25 × 10−11 1.43 × 10−11 939 1.15 1.13 × 10−11 1.74 × 10−11 1.16 × 10−11 1.32 × 10−11 888 1.24 1.08 × 10−11 1.58 × 10−11 1.08 × 10−11 1.22 × 10−11

7.5 Discussion

7.5.1 Mechanism Performances

The performance of a mechanism can be evaluated by how well the experimentally- determined rate constant for Reaction (7.1) from a given mechanism matches the original rate constant used in that mechanism. Figure 7.6 shows the overall rate constants for Reaction (7.1) from the Grana et al. [40] and Sarathy et al. [91] mechanisms. The original rate constant for Reaction (7.1) from the Van Geem et al. [37] mechanism is not shown because it is over an order of magnitude slower than the data shown in Figure 7.6. The rate constant for Reaction (7.1) determined from the experimental data using the secondary chemistry of the Sarathy et al. mechanism is within 10% of their original rate constant value; therefore, the Sarathy et al. mechanism best simulates the current measured OH time-histories. The Grana et al. mechanism also appears to be capable of simulating OH time-histories in reasonable agreement with the current data, as their original rate constant for Reaction (7.1) is within 25% of the experimentally-determined rate constant using the Grana et al. secondary chemistry. The Van Geem et al. [37] mechanism uses a rate constant for Reaction (7.1) an order of magnitude slower than all of the experimentally-determined values of the rate constant for Reaction (7.1). Therefore, OH time-histories simulated using the Van 124 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL

Geem et al. mechanism will provide poor agreement with the current data and the simulated OH time-history using their mechanisms will predict an OH decay much slower than the measured values. While the value of the rate constant for Reac- tion (7.1) in the Van Geem et al. mechanism appears to be incorrect, there is no compelling evidence to suspect that the rate constants for important secondary reactions in their mechanism are subject to the same degree of inaccuracy. Therefore, the value for the rate constant for Reaction (7.1) determined from the current data using the secondary chemistry in the Van Geem et al. mechanism may be a reason- ably accurate evaluation of the actual rate constant, and using this rate constant determination in the Van Geem et al. mechanism would signiﬁcantly improve their kinetic mechanism. While comparison of the original rate constant for Reaction (7.1) used in a mechanism with the experimentally-determined rate constant using the same mechanism can illustrate the performance of a mechanism, no insight can be gained on the accuracy of any speciﬁc rate constants. This is because of the number of important secondary reactions involved in the simulation of the OH time-history, as illustrated by the OH sensitivity analysis shown in Figure 7.2. Excellent performance of a mechanism could indicate the use of accurate rate constants; however, this could also be due to errors in rate constants fortuitously canceling out. Therefore, further studies into the important branching ratios discussed in this chapter are necessary to develop sec-butanol kinetic mechanisms that are accurate over a wide range of conditions and experimental validation targets.

7.5.2 Low-temperature Rate Constants

The current determination of the rate constant for Reaction (7.1) can be compared with data presented in the literature [118–120] regarding the rate constant at atmospheric-relevant conditions (near 298 K). Figure 7.7 presents an Arrhenius plot of the current data (the current data represents the average of the rate constant av. for Reaction (7.1) determined using the three mechanisms, where ln(k7.1) was taken 7.5. DISCUSSION 125

to be the average of the three ln(k7.1) values determined from each mechanism determination at each temperature point) compared with recommendations for the overall rate constant from the literature from atmospheric-relevant studies. Eq. 7.2 presents an empirical 3-parameter ﬁt to the data for the rate constant for Reaction (7.1).

! 1123 k = 4.95 × 10−20T 2.66 exp + cm3molecule−1s−1 (Eq. 7.2) 7.1 T [K]

Eq. 7.2 is valid for the temperature range 263 to 1178 K. The low-temperature data exhibit a negative temperature dependence, also seen in the iso-butanol data examined in Chapter 6. Therefore, the rate constant at low temperatures may be pressure and bath gas dependent and caution must be taken when applying the current expression for the rate constant for Reaction (7.1) at pressures outside of the range of the data presented in the literature [118–120] for temperatures under ∼400 K.

Reaction (7.1): CH CH(OH)CH CH + OH -> Products 3 2 3 1000 K 500 K 333 K 250 K 3 Experimental Data ]

-1 2.5 Current work (average) s

-1 Jiminez et al. (2005) 2 Baxley and Wells (1998) Chew and Atkinson (1996) 1.5 molecule 3

cm 1 -11 [10 7.1

k Current work (3-parameter fit) Atkinson (Structure-activity Relationship) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1000/T [K-1]

Figure 7.7: Arrhenius plot of the rate constant for Reaction (7.1). The data from the current work is the average of the rate constants determined using the three mechanisms discussed in this work, and the uncertainty limits of ±30% encompass the mechanism dependence of the rate constant determination. Also shown are data at atmospheric-relevant temperatures [118–120] and the rate constant estimated using the structure-activity relationship (SAR) of Atkinson and coworkers [20– 22, 90] extrapolated to high temperatures. 126 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL

The rate constant estimated using the structure-activity relationship (SAR) of Atkinson and coworkers [20–22, 90] that was empirically developed for rate constants for similar reactions at atmospheric-relevant temperatures is also shown on Figure 7.7 for comparison with the data. The rate constant predicted using the SAR method is ∼20% higher than the low-temperature data, and also fails to predict the current determination of the high-temperature rate constant within the ∼30% uncertainty limit. Discrepancies of this sort between experimentally-measured and SAR-estimated rate constants have been previously discovered in the literature for reactions of OH with alcohols [90, 115], with the most likely explanation that long-range eﬀects with respect to hydrogen atom abstraction at sites remote from the substituent group due to the formation of a hydrogen-bonded complex; the SAR rate constant estimation method considers only eﬀects of the alcohol group on the alpha and beta carbon sites. Therefore, the 3-parameter expression in Eq. 7.2 is recommended for a more accurate description of for the rate constant for Reaction (7.1).

7.6 Conclusions

OH time-histories were measured in shock-heated mixtures of tert-butylhydroperoxide (TBHP) with sec-butanol in excess, diluted in argon. Rate constants were determined for the overall reaction of OH with sec-butanol by fitting simulated OH time-histories from modified detailed mechanisms of sec-butanol combustion from the literature to the measured data, using the overall rate constant of interest as the free parameter. The rate constant determination from the measured OH time-histories was found to be mechanism dependent, and analysis of the differences in the mechanisms indicate that the reaction pathways of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals need to be better understood. An Arrhenius expression for the rate constant for the overall reaction of OH with sec-butanol is suggested and a ±30% uncertainty is ascribed to account for the mechanism dependence of the rate constant determination. The measured OH time-histories are best simulated using the Sarathy et al. [91] mechanism. While this agreement could indicate the use of accurate rate constants in this mechanism, the agreement could also be attributed to errors in rate constants 7.6. CONCLUSIONS 127

canceling out in the simulation, therefore, further studies on the rate constants of important secondary reactions in sec-butanol kinetics are necessary to develop accurate sec-butanol kinetic mechanisms. The structure-activity relationship (SAR) of Atkin- son and coworkers [20–22, 90] overpredicts both previously reported low-temperature (near 298 K) measured rate constants for the reaction of OH with sec-butanol, and also the current high-temperature determination. A 3-parameter modiﬁed Arrhenius expression is developed to correctly predict both the current high-temperature rate constant data and the low-temperature data from the literature. 128 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL Chapter 8

Reaction of OH with tert-Butanol

8.1 Introduction

8.1.1 Background and Motivation

Gasoline-grade tert-butanol, (CH3)3COH, is a common fuel additive used as an octane booster to prevent knock in spark-ignition engines. The addition of tert-butanol to traditional hydrocarbon-based automotive fuels also serves to reduce air pollu- tant emissions such as CO, NOx, and soot. Previous experimental studies on the combustion kinetics of tert-butanol include shock tube ignition delay [31, 35], shock tube pyrolysis [121], premixed [43] and diffusion [122] flames, and speciation measurements during oxidation [122, 123] and pyrolysis [124] in flow reactors. Several detailed kinetic mechanisms have been developed [31, 37, 40, 91] for the high-temperature oxidation of tert-butanol using these experimental studies as validation targets. While the existing detailed mechanisms perform well in predicting some of these global kinetic targets, many of the rate constants in the tert-butanol oxidation mechanisms are poorly known and vary by orders of magnitude between mechanisms. To the author’s knowledge, no high-temperature experimental studies have yet been carried out that are specifically designed with high sensitivity to rate constants for important combustion-relevant tert-butanol reactions. An important reaction in detailed high-temperature oxidation mechanisms for

129 130 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

any fuel is the reaction of the fuel with the hydroxyl (OH) radical. For tert-butanol, this reaction proceeds via the two reaction channels described by Reactions (8.1a) and (8.1b).

(CH3)3COH + OH −→ (CH3)2(CH2)COH + H2O (8.1a)

−→ (CH3)3CO + H2O (8.1b)

The overall rate constant for Reaction (8.1) has been measured using relative-rate methods by Cox and Goldston [125], and Wu et al. [111], and absolute measurement methods by Wallington et al. [126], Teton et al. [127], and Saunders et al. [128] at atmospheric-relevant conditions. These rate constant measurements span the limited temperature range 240 to 440 K, making it diﬃcult to accurately extrapolate the rate constant for Reaction (8.1) to combustion-relevant temperatures.

Overall rate constant measurements for Reaction (8.1) at elevated temperatures are complicated by the catalytic conversion of alcohols to alkenes, a phenomena ﬁrst discussed by Hess and Tully [129], during which hydrogen-atom abstraction by OH from beta-sites in alcohols produce an hydroxyalkyl intermediate that rapidly disso- ciates to OH + alkene at elevated temperatures (for ethanol, this occurs at T > 500 K). Reaction (8.1a) is the beta-site abstraction for tert-butanol, and this reaction channel is expected to dominate the overall reaction, thus complicating measurement of the overall reaction rate constant because of the possibility of the subsequent beta-scission decomposition by Reaction (8.2a) that can rapidly reproduce an OH radical at elevated temperatures. To make matters more complex, Reaction (8.2b) is a non-OH-forming reaction that competes with Reaction (8.2a).

(CH3)2(CH2)COH −→ (CH3)2C−CH2 + OH (8.2a)

−→ (CH3)(CH2)COH + CH3 (8.2b)

Figure 8.1 shows the reaction pathways of tert-butanol after reaction with OH. The tert-butoxyl radical product of Reaction (8.1b) will rapidly decompose via Re- action (3.2) to ﬁnal products of a methyl radical and acetone molecule; these ﬁnal 8.1. INTRODUCTION 131

products do not include OH radicals and thus do not interfere with rate constant measurement. Because of the subsequent OH-producing nature of Reaction (8.1a), measuring the overall rate constant for the reaction of OH with tert-butanol becomes more challenging at elevated temperatures.

+OH OH O O + CH3 (8.1b) (3.2) +H2O +OH

(8.1a) brOH = k8.1a/(k8.1a+k8.1b)

CH + OH OH (8.2b) 3 +H2O

(8.2a) brβ = k8.2a/(k8.2a+k8.2b)

OH-consuming reaction + OH OH-producing reaction Other secondary reaction

Figure 8.1: Dominant reaction pathways of tert-butanol after reaction with OH. OH-consuming reactions are shown with red arrows, and OH-producing reactions are shown with green arrows. Important branching ratios that describe competition between OH-producing and non-OH-producing pathways are also deﬁned.

Overall rate constant measurements for the reaction of OH with alcohols above 18 500 K have been done using isotopic substitution for the OH precursor (H2 O) in heated reactor experiments by Hess and Tully [129] for ethanol (up to 599 K) and Dunlop and Tully [130] for 2-propanol (up to 745 K). Shock tube experiments using tert-butylhydroperoxide (TBHP) as an OH precursor have become a common technique for rate constant measurements in the temperature range 800 to 1300 K, as illustrated in the previous chapters of this thesis. In the case of the shock tube experiments employing TBHP for determining the overall rate constant for reaction of OH with alcohols, 18O-substituted precursors or alcohols are diﬃcult to obtain, and deuterium-substituted alcohols can undergo ROD→ROH exchange, which introduces diﬃculties in knowing the actual fraction of deuterium-substituted alcohol in the 132 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

experiments. Therefore, experimental determinations of the overall rate constant for reaction of OH with alcohols in shock tubes at temperatures above 800 K have relied on kinetic modeling to account for secondary reactions, as was done in the previous chapters of this thesis.

8.1.2 Objectives of the Current Chapter

This chapter extends the work in the previous chapters on reactions of OH with butanol and presents the results of OH time-history measurements in shock tube experiments sensitive to the rate constant for the reaction of OH with tert-butanol. Dilute mixtures of TBHP, as a fast source of OH, with tert-butanol in excess were heated behind reflected shock waves, and narrow-linewidth laser absorption by OH was employed for quantitative time-resolved measurements of the pseudo-first-order OH time-history decay. The pseudo-first-order rate constant was determined, and the net OH rate of decay due to reaction with tert-butanol is presented and used to validate and refine the performance of three recent kinetic mechanisms of tert- butanol. Additionally, rate constants for secondary reactions were estimated based on the information available in the literature and an overall rate constant for the reaction of OH with tert-butanol is suggested.

8.1.3 Organization of this Chapter’s Results

The presentation of the results and discussion regarding the experimental work carried out for this chapter follow a unique order because of the complexity of the problem. Section 8.2 presents the details of the experiments performed for this chapter. Sec- tion 8.3 presents the experimental results as pseudo-first-order OH decay rates and reports the observed net rate of OH removal during the experiments. Section 8.4 introduces a kinetic model developed to account for secondary reactions in the tert- butanol and TBHP kinetic system. Using this mechanism, a net rate of OH removal due to reaction with tert-butanol (without influence of TBHP as the OH precursor) is derived. Section 8.5 presents a discussion on the estimation of several key branching ratios from the information available in the literature; and finally, in Section 8.6, the 8.2. EXPERIMENTAL 133

overall rate constant for the reaction of OH with tert-butanol is inferred from the data and the results are compared to the literature.

8.2 Experimental

The shock tube and laser diagnostics described in Chapter 2 of this thesis were used for the experimental work described in this chapter. In addition to the chemicals described in Chapter 2 (TBHP/water solution 70%, by weight TBHP, and argon gas), anhydrous tert-butanol from Sigma Aldrich, ≥99.5% purity, was used in the mixture preparation for the experiments in this chapter. Because the melting point of tert-butanol is 23-26◦C, the laboratory room temperature was raised to greater than 26◦C during the experiments of this chapter to facilitate the production of tert- butanol vapors and to ensure that the tert-butanol vapor remained in the vapor phase throughout the experiments and prevent the condensation or solidiﬁcation onto the facility surfaces. OH time-histories were measured from 902 to 1197 K for two mixture compositions: 445 ppm tert-butanol with 17 ppm TBHP, and 300 ppm tert-butanol with 14 ppm TBHP, both mixtures dilute in argon. The temperature range of the current experiments was constrained by slow TBHP decomposition at temperatures less than 900 K and tert-butanol decomposition at temperatures above 1200 K. All experiments were taken at reﬂected-shock pressures near 1 atm.

8.3 Net OH Removal Rates

A sample OH time-history measurement trace at 943 K is shown in Figure 8.2. Subse- quent to the initial OH formation, the OH time-history follows an exponential decay, and low-noise measurements of the OH time-history are observed for times up to about 200 µs. At temperatures under 1000 K, the OH formation occurs over a ﬁnite time interval (up to 30 µs at 907 K); at higher temperatures the OH formation time is shorter. Using a pseudo-ﬁrst-order analysis, similar to the one described in Section 4.3.1, a 134 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

Current data k (1 - br *br ) = 1.87x10-12 8.1 OH β cm3 molecule-1s-1 k (1 - br *br ) +30% 1 8.1 OH β k (1 - br *br ) -30% 8.1 OH β 10 Reaction (8.1): (CH ) COH + OH -> Products 3 3

brOH = k8.1a / (k8.1a + k8.1b) br = k / (k + k ) β 8.2a 8.2a 8.2b

OH mole fraction [ppm] 943 K, 1.20 atm 445 ppm (CH ) COH, 17 ppm TBHP 3 3 1 0 40 80 120 160 200 Time [μs]

Figure 8.2: Measured OH time-history at 943 K on a semi-logarithmic plot; an exponential decay is seen after the initial formation of OH (∼30 µs). Also shown is the best-fit simulated OH time-history with the current mechanism, and simulated OH time-histories with k8.1 · (1 − brOH · brβ) perturbed by ± 30%. The simulated OH time-history with the perturbed k8.1 · (1 − brOH · brβ) is independent of whether k8.1 or brβ is perturbed for an overall perturbation of 30%. pseudo-first-order rate constant for the net OH removal can be defined by by Eq. 8.1, 0 where k is the pseudo-first-order rate constant, xOH is the OH mole fraction, and t is time. Measurements of k0 were determined from each data trace by taking the slope of a linear least-squares fit of ln xOH vs. t using the data from the time after the complete decomposition of TBHP to 200 µs. A second-order rate constant can also be defined by Eq. 8.2, where k00 is a second-order rate constant for the net removal rate of OH, and [(CH3)3COH] is the concentration of tert-butanol.

d(ln x ) k0 = − OH (Eq. 8.1) dt −1 d(ln x ) k00 = · OH (Eq. 8.2) [(CH3)3COH] dt

The pseudo-ﬁrst-order rate constant and second-order rate constant for the net removal rates of OH are listed in Table 8.1 for each experimental temperature. These rate constants describe the net OH removal in the current experiments, including the 8.4. KINETIC MODELING 135

reaction of OH with tert-butanol and several secondary reactions involving OH radicals. Further analysis using kinetic modeling is needed to determine the rate constant for the reaction of OH with tert-butanol because the net removal rate of OH is not the same as the rate constant for Reaction (8.1). This is due to the inﬂuence of Reac- tion (8.2a) as an OH-producing secondary reaction and to other secondary reactions associated with the use of TBHP as the OH precursor such as Reactions (3.5), (3.3), and (3.4).

Table 8.1: Pseudo-first-order and second-order rate constants determined for each experimental temperature. The pseudo-first-order and second-order rate constants are defined by Eq. 8.1 and Eq. 8.2, respectively, and describe the measured OH decay rate, including the influence of the final TBHP decomposition products.

Mixture T [K] P [atm] k0 [s−1] k00 [cm3molecule−1s−1] 307 ppm tert-butanol 1197 0.93 1.04 ×104 5.93 ×10−12 15 ppm TBHP 1166 0.98 0.97 ×104 5.11 ×10−12 1162 0.97 1.00 ×104 5.31 ×10−12 1113 0.99 1.07 ×104 5.29 ×10−12 1079 1.03 0.89 ×104 4.17 ×10−12 1020 1.05 0.92 ×104 3.97 ×10−12 974 1.15 1.09 ×104 4.10 ×10−12 445 ppm tert-butanol 1058 1.06 1.49 ×104 6.64 ×10−12 17 ppm TBHP 1004 1.13 1.40 ×104 5.53 ×10−12 962 1.16 1.44 ×104 5.30 ×10−12 943 1.20 1.42 ×104 4.98 ×10−12 902 1.21 1.46 ×104 4.83 ×10−12

8.4 Kinetic Modeling

A detailed mechanism describing the kinetics of the reaction of OH with tert-butanol and subsequent secondary reactions was compiled using the alkane/TBHP mechanism from Chapter 4 as a base mechanism that accurately describes the secondary reactions due to the presence of TBHP as the OH precursor. Reactions (8.1a), (8.1b), (8.2a), and (8.2b) were added to the alkane/TBHP mechanism to account for the tert- butanol-related reactions. Rate constants for these reactions were initially taken from the published mechanisms on tert-butanol [37, 40, 91] for initial examination of OH 136 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

sensitivity; subsequently, these rate constants were updated to values as discussed in the Section 8.5. This kinetic mechanism contains all the reactions expected to occur under the experimental conditions of the current work; however, this mechanism may not fully describe experiments outside of the current experimental conditions.

Brute force sensitivity of the pseudo-first-order rate constant k0 was computed using the final current mechanism for the experimental conditions in Figure 8.2, and the results are shown in Figure 8.3 for the top nine reactions that influence the sensitivity. The brute force sensitivity is defined by Eq. 8.3.

0 ∆k ki · 0 (Eq. 8.3) ∆ki k

The simulated pseudo-ﬁrst-order rate constant is predominately sensitive to the rate constants of Reactions (3.3), (3.4), (8.1a), (8.1b), (8.2a), and (8.2b), and minor contribution is also present from reactions of CH3 +OH −→ CH3OH, CH3 +CH3 −→ C2H6, and iC4H8 + OH −→ Products. Reactions (3.3), (3.4), CH3 + OH −→ CH3OH, and

CH3 + CH3 −→ C2H6 are all important in the TBHP sub-mechanism, which was validated in Chapter 3. The only tert-butanol-related reactions that contribute sig- niﬁcantly to the sensitivity are Reactions (8.1a), (8.1b), (8.2a), and (8.2b). Because of the high sensitivity of the simulated pseudo-ﬁrst-order rate constant to the rate constants for Reactions (8.2a), and (8.2b), the rate constant for Reaction (8.1) cannot be determined from the measured OH time-histories without accurate rate constants for Reactions (8.2a) and (8.2b), or at least accurate knowledge of the relative rate constants between these reactions.

A rate of production (ROP) analysis for the current experimental conditions at 943 K indicates that 80% of the gross OH consumption (considering only OH- consuming reactions and not OH-producing reactions) is due to Reaction (8.1); the results of the ROP analysis also indicate that a steady-state approximation is appropriate for the concentration of the (CH3)2(CH2)COH radical (i.e. d[(CH3)2(CH2)COH]/dt = 0). The ROP results are summarized in the reaction path diagram for OH shown in Figure 8.4. Based on this analysis, the kinetic rate law can 8.4. KINETIC MODELING 137

k 8.1a k 8.1b primary tert-butanol-related k kinetics 8.2a k 8.2b k 3.3 TBHP-related kinetics k 3.4 k CH +OH+M 3 k CH +CH 3 3 k OH+iC H secondary tert-butanol kinetics 4 8 -50-250 255075 943 K, 1.20 atm Brute Force Pseudo-first-order 1 445 ppm (CH ) COH, Rate Constant Sensitivity: 3 3 (Δ k' / Δk ) * (k / k' ) x 100% 17 ppm TBHP i i

Figure 8.3: Brute force sensitivity for the pseudo-ﬁrst-order rate constant using the current kinetic mechanism for the experimental conditions in Figure 8.2. be written as Eq. 8.4 for the rate of change of OH concentration in time.

! n d[OH] k8.1a k8.2a X − = k 1 − [(CH ) COH][OH] + k [X ][OH] dt 8.1 k + k k + k 3 3 i i 8.1a 8.1b 8.2a 8.2b i=5 (Eq. 8.4)

In Eq. 8.4, Xi represents secondary species that can react with OH, such as TBHP,

CH3, and acetone. Eq. 8.4 indicates that the pseudo-ﬁrst-order rate constant determined in Section 8.3 (k0 listed in Table 8.1) can be expressed by Eq. 8.5, where the branching ratios brOH and brβ are deﬁned by Eq. 8.6 and Eq. 8.7, respectively, and illustrated in Figure 8.1.

n 0 X k = k8.1 · (1 − brOH · brβ)[(CH3)3COH] + ki[Xi] (Eq. 8.5) i=5

brOH = k8.1a/(k8.1a + k8.1b) (Eq. 8.6)

brβ = k8.2a/(k8.2a + k8.2b) (Eq. 8.7) 138 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

Both branching ratios brOH and brβ each represent competition between OH- producing and non-OH-producing reaction pathways. Values for the branching ratios brOH and brβ will be discussed in Section 8.5. The last term in Eq. 8.5 contributes only 20% of all positive OH consumption at 943 K according to the kinetic mechanism; at the same temperature, however, this term contributes 53% of k0 because of the OH regeneration by Reaction (8.2a). While further experiments could be conducted with a higher initial tert-butanol-to- TBHP concentration ratio to minimize the contribution of secondary OH-consuming reactions, the validation of the base mechanism in Chapter 3 provides conﬁdence in n X the calculated contribution of ki[Xi]. i=5

(8.2a) 82% (8.2b) +other +t-butanol 18% non-OH 36% 53% products (3.3),(3.4),(3.5), etc. 20% OH 76% + (8.1a) OH

-butanol 4%

% of gross OH consumption (8.1b) % of net OH consumption

(3.2)

OH-consuming reaction CH3 + acetone OH-producing reaction Other secondary reaction 11%

Figure 8.4: OH reaction path diagram for the experimental conditions in Figure 8.2 from OH rate of production calculations at 45 µs, with brOH = 0.95 and brβ = 0.82. Reactions (8.1a) and (8.1b) contribute to a total of 80% of the gross OH consumption rate (considering only reactions that consume OH). Notice that Reaction (8.2a) is an OH-producing reaction that decreases the net OH decay rate that occurs subsequent to Reaction (8.1a). The overall contribution of Reactions (8.1a) and (8.1b) to the net (observed) OH consumption rate, therefore, is only 47%. 8.4. KINETIC MODELING 139

8.4.1 Net OH Removal Rate by Reaction with tert-Butanol

The net OH removal rate constant due to reaction with tert-butanol can be described by the product k8.1 ·(1−brOH ·brβ). This term is independent of any influence of TBHP as the OH precursor, thus it differs from the second-order rate constant k00. The value of k8.1 · (1 − brOH · brβ) is determined using the detailed mechanism to simulate OH time-histories to fit the experimental data, where the parameters k8.1, brOH, and brβ are adjusted as free parameters. Obviously, the value of k8.1 required to simulate an

OH time-history that ﬁts the experimental data is dependent on the values of brOH, and brβ in the mechanism. With the current kinetic mechanism, however, it was found that for any value of brOH from 0.5 to 1.0 and brβ from 0.2 to 0.8, the value of k8.1 required to simulate an OH time-history that matches the measured OH time- history leads to a constant product of k8.1 · (1 − brOH · brβ) (assuming that the rate 5 −1 constants for k8.2a and k8.2b are of reasonable orders of magnitude ≥ 10 s ).

Figure 8.2 shows the simulated OH time-history from the kinetic mechanism that best matches the measured data, and the simulated OH time-history with the product of k8.1 · (1 − brOH · brβ) perturbed by ±30%. The simulated OH time-history with k8.1 · (1 − brOH · brβ) perturbed by ±30% is independent of which parameter in the product is perturbed to introduce an overall perturbation of ±30%. The values for the product of k8.1 · (1 − brOH · brβ) from the measured OH time-histories are listed in Table 8.2 and diﬀer from the values of k00 listed in Table 8.1 due to secondary reactions of OH, most of which occur due to the decomposition products of TBHP as the OH precursor. The measured values of k8.1 · (1 − brOH · brβ) are shown in Figure 8.5, and can be described by the Arrhenius expression in Eq. 8.8, valid for the temperature range 902 to 1197 K.

! 2435 k · (1 − br · br ) = 2.62 × 10−11 exp − cm3molecule−1s−1 (Eq. 8.8) 8.1 OH β T [K]

The overall rate constant for the reaction of OH with tert-butanol can be determined if the branching ratios brOH and brβ are known. Figure 8.6 presents values for 140 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

k8.1 for diﬀerent values of brOH and brβ, illustrating the sensitivity of the determination of k8.1 from the current data to the branching ratios. The closer the branching ratio brβ approaches the value 1.0, the more inﬂuence the branching ratio brOH has on the determination of the rate constant for Reaction (8.1). To the author’s knowledge, no studies, experimental or otherwise, have focused on the rate constants for the reactions involved in brOH and brβ or the branching ratios themselves. In the following section, values for the branching ratios are estimated given the information currently available in the literature.

1250 K 1111 K 1000 K 909 K 833 K Current data (solid line: fit)

] Calculated from Mechanisms -1 Sarathy et al. (2012) s ) β -1 Grana et al. (2010) br * 10 Van Geem et al. (2010) OH br molecule

3 * (1 - cm 8.1 -12 k [10 1

0.8 0.9 1.0 1.1 1.2 1000/T [K-1]

Figure 8.5: Arrhenius plot of the product of k8.1 · (1 − brOH · brβ) determined at each experimental temperature from the measured OH time-histories, and an Arrhenius ﬁt to the data. The product k8.1 · (1 −brOH · brβ) describes the net rate of OH decay due to the reaction OH + tert-butanol. Also shown is the product k8.1 · (1 − brOH · brβ) computed using the rate constants from three detailed mechanisms for high-temperature tert-butanol oxidation [37, 40, 91]. 8.4. KINETIC MODELING 141

Reaction (8.1): (CH ) COH + OH -> Products 3 3 1250 K 1111 K 1000 K 909 K 833 K

br = 0.95, br = -4.37x10-4T + 1.23 OH β ] -1 s

-1 10

brβ=0.8 molecule 3

brβ=0.6 cm -12 brβ=0.4

[10 br = 1.00 br =0.2 OH β 8.1 k brOH = 0.95

brOH = 0.90 1 0.8 0.9 1.0 1.1 1.2 1000/T [K-1]

Figure 8.6: Arrhenius plot of the overall rate constant for Reaction (8.1) with various values for brOH and brβ illustrating the sensitivity of the rate constant for Reaction (8.1) to these branching ratios. Also shown is the rate constant for Reaction (8.1) determined from the experiments assuming the branching ratios evaluated in Section 8.5.

Table 8.2: Rate constants determined for each experimental temperature. The product k8.1 · (1 − brOH · brβ) describes the rate of OH decay due to reaction with tert-butanol, independent of the OH precursor. The branching ratio brβ and overall rate constant for Reaction (8.1) determined using the analysis discussed in Sections 8.5 and 8.6 are also given. ‡Units of second order rate constants is [cm3molecule−1s−1].

‡ ‡ Mixture T [K] P [atm] k8.1 · (1 − brOH · brβ) brβ k8.1 307 ppm tert-butanol 1197 0.93 3.48 ×10−12 0.71 1.06 ×10−11 15 ppm TBHP 1166 0.98 3.22 ×10−12 0.72 1.02 ×10−11 1162 0.97 3.24 ×10−12 0.72 1.03 ×10−11 1113 0.99 2.87 ×10−12 0.74 0.98 ×10−11 1079 1.03 2.64 ×10−12 0.76 0.94 ×10−11 1020 1.05 2.44 ×10−12 0.78 0.96 ×10−11 974 1.15 2.29 ×10−12 0.80 0.97 ×10−11 445 ppm tert-butanol 1058 1.06 2.79 ×10−12 0.77 1.03 ×10−11 16 ppm TBHP 1004 1.13 2.17 ×10−12 0.79 0.87 ×10−11 962 1.16 2.07 ×10−12 0.81 0.90 ×10−11 943 1.20 1.87 ×10−12 0.82 0.84 ×10−11 902 1.21 1.81 ×10−12 0.84 0.88 ×10−11 142 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

8.5 Branching Ratio Determinations

8.5.1 Evaluation of brOH

The branching ratio brOH represents the fraction of the reaction of OH with tert- butanol that proceeds via Reaction (8.1a), the product channel that leads to subsequent OH production. Reaction (8.1a) is the result of hydrogen-atom abstraction from the tert-butyl group, where nine hydrogen atoms exists, each with a approximately equal probability of abstraction. The other channel of the reaction of OH with tert-butanol, Reaction (8.1b), results from hydrogen-atom abstraction from the alcohol group where there is only one hydrogen atom available for abstraction. The rate of abstraction of the hydrogen atom on the alcohol group via Reaction (8.1b) is expected to be slower than the abstraction of a single hydrogen on the tert-butyl group based on bond energy arguments. Therefore, the value of the branching ratio brOH is expected to be no less than 9/(9 + 1), or, in other words, between 0.9 and 1.0. This is consistent with the branching ratio calculated from the rate constants for Reactions (8.1a) and (8.1b) used in the Grana et al. [40] and Sarathy et al. [91] butanol oxidation mechanisms. A branching ratio brOH = 0.95 will be assumed in the current work with a conservative uncertainty of ±5%.

8.5.2 Evaluation of brβ

The branching ratio brβ represents the fraction of the (CH3)2(CH2)COH radicals that decomposes via Reaction (8.2a) to regenerate an OH radical. Figure 8.7 shows the temperature dependence of brβ calculated with the rate constants for Reac- tions (8.2a) and (8.2b) from the tert-butanol oxidation mechanisms of Van Geem et al. [37] and Sarathy et al. [91]. The detailed mechanism of Grana et al. [40] does not include Reaction (8.2b), however, a non-OH-producing decomposition channel of (CH3)2(CH2)COH −→ CH3COCH3 + CH3 is included in the mechanism, and the products of this reaction are not expected to significantly affect the simulated OH time-history differently than the products of Reaction (8.2b). Thus, a branching ratio 8.5. BRANCHING RATIO DETERMINATIONS 143

brβ can still be calculated from the Grana et al. mechanism representing the fraction of the (CH3)2(CH2)COH radical that decomposes to form an OH radical versus other non-OH products; this calculated value from the Grana et al. mechanism is also shown in Figure 8.7. The three mechanisms predict values for the branching ratio brβ that vary by up to a factor of seven over the current experimental temperature range, motivating a detailed estimation for the branching ratio brβ based on the literature.

1250 K 1111 K 1000 K 909 K 833 K 1.0

) 0.8

8.2b Current recommendation k

+ Sarathy et al. (2012) 0.6 Grana et al. (2010) 8.2a

k Van Geem et al. (2010)

/ ( 0.4 8.2a k = β 0.2 br

0.0 0.8 0.9 1.0 1.1 1.2 1000/T [K-1]

Figure 8.7: The temperature-dependent branching ratio brβ computed using the rate constants in three detailed mechanisms from the literature, and the current recommendation of brβ = −4.37 × 10−4T + 1.23 based on rate constants from Bozzelli and coworkers [131, 132].

Bozzelli and coworkers [131, 132] have several works that suggest rate constants relevant to estimating brβ. Chen and Bozzelli [131] analyzed the mechanism of tertiary butyl oxidation and suggest a high-pressure limit rate constant for Reaction (8.2b) based on thermodynamic properties from THERM group additivity and the addition rate constant for OH with iso-butene from Mallard et al. [133]. QRRK analysis was used to determine the rate constant for Reaction (8.2b) at 1 atm; their 1-atm rate constant for Reaction (8.2b) is given in Eq. 8.9. Sun and Bozzelli [132] use canonical transition-state theory to calculate the high-pressure-limit unimolecular rate constant for the decomposition of the neo-pentyl radical to iso-butene plus a methyl radical. Using the rate constant and thermodynamic data in their publication, the rate constant for the addition reaction of methyl to iso-butene can be computed. In the 144 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

current work, the assumption is made that the rate constant of the addition reaction of a methyl radical plus iso-butene is equivalent to the rate constant for the addition reaction of a methyl radical plus propen-2-ol, the reverse of Reaction (8.2b), therefore, a calculation of the reverse rate constant yields the high-pressure-limit rate constant for Reaction (8.2b). To compute the reverse rate constant, the thermodynamic data for propen-2-ol were estimated from the group additivity values of Khan et al. [134] and the thermodynamic data for the (CH3)2(CH2)COH and the methyl radicals were taken for from Chen and Bozzelli [131]. To estimate the pressure dependence of the rate constant for Reaction (8.2b), the Kassel integral was applied to the high-pressure limit rate constant (see Appendix E) using S = 14 (chosen as the parameter that predicts the pressure-dependence for the rate constant for Reaction (8.2a) calculated by Chen and Bozzelli using a QRRK method). The 1-atm rate constant inferred for Reaction (8.2b) is given by Eq. 8.10.

Using rate constants based on the work of Bozzelli and coworkers [131, 132], the temperature-dependent branching ratio brβ is estimated to be bound between 0.70 and 0.85 in the current experimental temperature range, and the current estimated value is shown in Figure 8.7. The current recommendation for the branching ratio brβ can be expressed by Eq. 8.11.

20612 k = 2.33 × 1045 · T −9.88 · exp − s−1 (Eq. 8.9) 8.2a T [K] 22035 k = 2.27 × 1041 · T −8.53 · exp − s−1 (Eq. 8.10) 8.2b T [K] −4 brβ = −4.37 × 10 T + 1.23 (Eq. 8.11)

The current evaluation of brβ shows excellent agreement with the corresponding branching ratio calculated using the rate constants in the Sarathy et al. [91] mechanism. However, the performance of the Sarathy et al. [91] mechanism, or any of the mechanisms examined, also depends on the mechanism’s rate constant of Reac- tion (8.1a) and (8.1b), which are typically determined independently of the branching ratio brβ. The performance of each of the mechanisms examined is discussed in the Section 8.6.1. 8.6. OVERALL RATE CONSTANT DETERMINATION 145

8.6 Overall Rate Constant Determination

With knowledge of the branching ratios brOH and brβ, the overall rate constant for Re- action (8.1) can be determined from the measurements of the net rate of OH removal from reaction with tert-butanol that were presented in Section 8.4.1. The overall rate constant for each of the experimental temperatures is shown in Figures 8.6 and 8.8, and can be summarized in Arrhenius form by Eq. 8.12, valid for the temperature range 902 to 1197 K.

! 725 k = 1.91 × 10−11 · exp − cm3molecule−1s−1 (Eq. 8.12) 8.1 T [K]

The rate constants determined for each experimental temperature are also presented in Table 8.2.

Reaction (8.1): (CH ) COH + OH -> Products 3 3 1000 K 500 K 333 K 250 K

] Current work -1 3-parameter fit s -1 10 Literature Data Wu et al. (2003) Saunders et al. (2002) Teton et al. (1996) Wallington et al. (1988) molecule 3 Cox and Goldstone (1982) cm 1

-12 Mechanisms Sarathy et al. (2012)

[10 Grana et al. (2010) 8.1 Van Geem et al. (2010) k SAR 0.1 Bethel et al. (2001) 1234 1000/T [K-1]

Figure 8.8: Arrhenius plot of experimental determinations for the overall rate constant for the −20 reaction of OH with tert-butanol and the best-ﬁt 3-parameter expression of k8.1 = 8.93 × 10 ·T 2.60 exp(450/T [K]) cm3molecule−1s−1. Also shown is comparison with the corresponding rate constant used in three detailed mechanisms [37, 40, 91] and the structure-activity relationship of Atkinson and coworkers [20–22] with the most up-to-date parameters from Bethel et al. [90]. 146 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

An uncertainty analysis for the current measurements of the net rate of OH removal from reaction with tert-butanol was conducted, and an overall ±14% uncer-

tainty was found for the product k8.1 · (1 − brOH · brβ), accounting for uncertainty in temperature, pressure, initial TBHP and tert-butanol concentration, laser noise, impurities, unimolecular reaction of tert-butanol, and rate constants for secondary reactions in the TBHP mechanism. The uncertainty in the determination of the rate constant for Reaction (8.1), however, is larger due to the uncertainties in the branch-

ing ratios brOH and brβ. If the uncertainty of each of the rate constants from the work of Bozzelli and coworkers [131, 132] is taken to be a factor of two, the total uncertainty in the rate constant for Reaction (8.1) is approximately a factor of two. The largest uncertainty factor in the rate constant determination is the uncertainty

in the branching ratio brβ; thus, further studies on this branching ratio or the rate constants for Reactions (8.2a) and (8.2b) are recommended.

8.6.1 Comparisons to Mechanism Predictions

The accuracy of three detailed mechanisms containing tert-butanol oxidation kinetics was examined in regards to their ability to predict the net rate of OH removal due to reaction with tert-butanol, and the overall rate constant used for Reaction (8.1) in

each mechanism was also assessed. Figure 8.5 shows the product of k8.1 ·(1−brOH ·brβ) determined from the rate constants in the Van Geem et al. [37], Grana et al. [40], and Sarathy et al. [91] mechanisms in comparison with the currents measurements.

Agreement of the product of k8.1 · (1 − brOH · brβ) in a mechanism with the current determination of the product is the indicator of whether the OH time-histories would be correctly simulated under the current conditions. The Van Geem et al. mechanism has rate constants for Reactions (8.1a), (8.1b), (8.2a), and (8.2b) that lead to a value

of k8.1 · (1 − brOH · brβ) that best matches the current measured value, and thus this mechanism is capable of predicting within 20% the measured net rate of OH removal from the pseudo-ﬁrst-order reaction of OH with tert-butanol. The Sarathy et al. mechanism also will show good agreement in the prediction of the OH time-history near 1200 K; however, the mechanism predicts a net pseudo-ﬁrst-order rate constant 8.6. OVERALL RATE CONSTANT DETERMINATION 147

that is a factor of two too slow near 900 K. The Grana et al. mechanism predicts a pseudo-ﬁrst-order rate constant that is a factor of four faster than the current data.

Because a mechanism may correctly predict the OH time-histories of the current measurements with only the correct product of k8.1 · (1 − brOH · brβ), there is a possibility for large errors to be present in the individual rate constants that cancel out. Because the rate constant for Reaction (8.1) in a mechanism is typically determined independently from the rate constants included in the branching ratio brβ, both the rate constant for Reaction (8.1) and the branching ratio brβ must be examined, and reasonable values for these parameters should be used to improve the mechanism’s performance over a wide range of conditions. As was previously shown in Figure 8.7, the Sarathy et al. [91] mechanism uses a value for brβ in best agreement with the current determination, while the Van Geem et al. [37] and Grana et al. [40] mechanisms used rate constants yielding brβ values much lower than the current determination. Figure 8.8 presents a comparison of the current determination of the rate constant for Reaction (8.1) in comparison to the value used in the three mechanisms from literature. Analysis of Figures 8.5, 8.7 and 8.8 together can elucidate the accuracy of the rate constants used in each mechanism.

The Grana et al. [40] mechanism uses an overall rate constant for Reaction (8.1) that is in good agreement with the current determination, considering the overall uncertainty (Figure 8.8); however, their value of the branching ratio brβ is much lower than the current determination (Figure 8.7). This suggests that updating the rate constant to Reaction (8.2a) and/or including Reaction (8.2b) as a non-OH-producing decomposition pathway of the (CH3)2(CH2)COH radical in the Grana et al. mechanism would improve the mechanism’s ability to predict the current measured OH time-histories.

The overall rate constant for Reaction (8.1) used in the Sarathy et al. [91] mechanism also shows good agreement with the current determination near 1200 K (Fig- ure 8.8), and the current determination of the branching ratio brβ is excellent agreement with their rate constants over the entire temperature range (Figure 8.7). How- ever, as the temperature decreases, the product of k8.1 · (1 − brOH · brβ) from the 148 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL

Sarathy et al. mechanism begins to deviate from the current data (Figure 8.5). In- creasing the overall rate constant for Reaction (8.1) in the Sarathy et al. mechanism at temperatures below 1200 K would improve the agreement between their model simulations and the current measured OH time-histories over the temperature range 900 to 1200 K. While the Van Geem et al. [37] mechanism predicts the measured net OH decay rate best (Figure 8.5), their mechanism uses an overall rate constant for Reaction (8.1) that is a factor of 3 slower than the current determination (Figure 8.8). Their branching ratio brOH is also over a factor of two smaller than the current recommendation of 0.95 that was presented in Section 8.5 based on counting hydrogen atoms and energy arguments. Changes to the relative rate constants between Reactions (8.1a) and (8.1b) that also increase the overall value of the rate constant for Reaction (8.1) are recommended for the Van Geem et al. mechanism to improve the accuracy of the rate constants used in their mechanism.

8.6.2 Comparisons to Low-temperature Literature

Measurements for the overall rate constant for the reaction of OH with tert-butanol have also been performed by Cox and Goldston [125], Wu et al. [111], Wallington et al. [126], Teton et al. [127], and Saunders et al. [128] in the temperature range 240 to 440 K, and these data are shown with the current determination of the rate constant for Reaction (8.1) in Figure 8.8. The three-parameter modiﬁed Arrhenius expression given in Eq. 8.13 ﬁts all the measured data for the temperature range 240 to 1197 K.

! 450 k = 8.93 × 10−20T 2.60 exp + cm3molecule−1s−1 (Eq. 8.13) 8.1 T [K]

The structure-activity relationship (SAR) of Atkinson and coworkers [20–22, 90] can be used to estimate the overall rate constant for the reaction of OH with tert- butanol (see Appendix D for details of the structure-activity relationship). Bethel et al. [90] shows that this method can predict the rate constant for Reaction (8.1) well at 298 K using their revised substituent factor that accounts for eﬀects of the 8.7. CONCLUSIONS 149

alcohol group as far as the β position, and comparison of the measured data with the SAR-calculated rate constant is shown in Figure 8.8. However, the SAR method is extrapolated to higher temperatures using the temperature-dependence suggested by Atkinson, the SAR-calculated rate constant overpredicts the rate constant for Reac- tion (8.1) at all temperatures above 298 K, including all temperatures in the current experimental conditions. This discrepancy is larger than the factor of two uncertainty in the current rate constant determination. Bethel et al. reports signiﬁcant disagree- ments of calculated rate constants with measurements for several hydroxy-containing compounds using the general approach of Atkinson, and therefore the disagreement of the SAR-calculated rate constant with the current high-temperature data is not unexpected.

8.7 Conclusions

OH time-histories were measured during the pseudo-first-order reaction of OH with tert-butanol, where the initial tert-butanol-to-OH concentration ratio was in excess of 30:1 and tert-butylhydroperoxide (TBHP) was used as the OH precursor. From these measurements, the following rates were determined: the net rate of pseudo-first- order OH decay, the net rate of OH decay due to reaction with tert-butanol (without influence of TBHP as the OH precursor), and the overall rate constant for the reaction of OH + tert-butanol → Products. To facilitate these rate constant determinations, a kinetic mechanism with TBHP and tert-butanol kinetics was developed, which included evaluation of important branching ratios in the kinetic system. Comparison of the current results to three tert-butanol combustion mechanisms [37, 40, 91] published in the literature reveal that improvements to each of these mechanism must be made to correctly simulate the measured OH time-histories. Recommendations are made on which key rate constant parameters in the mechanisms can be adjusted to best improve the agreement of the simulated OH time-history with the experimental data. To the author’s knowledge, this is the first experimental study on the high- temperature oxidation kinetics of tert-butanol designed with high-sensitivity to key rate constant parameters. 150 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL Chapter 9

Concluding Remarks

9.1 Summary of Work

The objective of the research presented in this thesis was to expand the experimental database of rate constants for reactions of the hydroxyl radical (OH) with diﬀerent types of organic compounds that are of current interest as transportation fuels. The organic compounds of interest fell in the category of either a normal alkane molecule or an isomer of the butanol molecule. Using a narrow-linewidth laser absorption diagnostic to quantitatively measure OH mole-fraction time-histories behind reﬂected shock waves, experiments were designed with high sensitivity to the rate constants of interest, including overall rate constants for Reactions (4.1), (4.2), (4.3), (5.1), (6.1), (7.1), and (8.1).

C5H12 + OH −→ Products (4.1)

C7H16 + OH −→ Products (4.2)

C9H20 + OH −→ Products (4.3)

CH3CH2CH2CH2OH + OH −→ Products (5.1)

(CH3)2CHCH2OH + OH −→ Products (6.1)

CH3CH(OH)CH2CH3 + OH −→ Products (7.1)

(CH3)3COH + OH −→ Products (8.1)

151 152 CHAPTER 9. CONCLUDING REMARKS

For all these experiments, tert-butylhydroperoxide (TBHP) was used as a fast source of OH radicals. To support the current research objectives, the rate constants for Reactions (3.1) and (3.3), which are important in simulating the OH time-history during decomposition of TBHP, were also measured.

(CH3)3COOH −→ (CH3)3CO + OH (3.1)

CH3 + OH −→ CH2(s) + H2O (3.3)

The rate constants for Reactions (3.1) and (3.3) can be described by Eq. 3.2 and Eq. 3.3, respectively.

! 18000 k = 3.57 × 10+13 exp − s−1 (Eq. 3.2) 3.1 T [K]

−11 3 −1 −1 k3.3 = 2.74 × 10 cm molecule s (Eq. 3.3)

The rate constants for Reactions (3.1) and (3.3) are valid over the experimental temperature ranges of this study (approximately 900 to 1400 K) and have an estimated uncertainty of ±30%.

The measured rate constants for the reactions involving the n-alkanes can be summarized in Arrhenius form by Eq. 4.5, Eq. 4.6, and Eq. 4.7 for a temperature range of approximately 860 to 1360 K.

These rate constant determinations improve upon similar previous works because of improved accounting for the kinetics of TBHP as an OH precursor. Furthermore, 9.1. SUMMARY OF WORK 153

systematic errors due to impurities and uncertainty in mixture composition were minimized using laser absorption techniques. The overall uncertainty in the rate constant measurements for Reactions (4.1), (4.2), and (4.3) are ±11% for temperatures from 1000 to 1364 K; the overall uncertainty increases with decreasing temperature below 1000 K, up to approximately ±23% at 869 K. The current results demonstrate that the structure-activity relationship (SAR) developed by Atkinson [20], updated with parameters by Kwok and Atkinson [22], can be extrapolated to temperatures up to 1364 K to accurately predict the overall rate constants for Reactions (4.1), (4.2), and (4.3). This SAR method is recommended for predicting the overall rate constant for reactions in the family of OH plus n-alkanes.

Rate constants for the reactions of OH with the isomers of butanol were determined from measured OH time-histories in shock-heated mixtures of OH (generated from fast decomposition of TBHP) with butanol in excess. To facilitate the rate constant determination and account for secondary chemistry, kinetic mechanisms that accurately simulate the OH time-history during TBHP decomposition were modi- ﬁed by the addition of important OH-forming and OH-consuming reactions related to butanol molecules. The results suggest the overall rate constants described by Eq. 5.2, Eq. 6.6, Eq. 7.1 and Eq. 8.12, valid over a temperature range of approximately 900 to 1200 K.

! 2505 k = 3.24 × 10−10 exp − cm3molecule−1s−1 (Eq. 5.2) 5.1 T [K] ! 2155 k = 1.85 × 10−10 exp − cm3molecule−1s−1 (Eq. 6.6) 6.1 T [K] ! 1550 k = 6.97 × 10−11 exp − cm3molecule−1s−1 (Eq. 7.1) 7.1 T [K] ! 725 k = 1.91 × 10−11 exp − cm3molecule−1s−1 (Eq. 8.12) 8.1 T [K]

Figure 9.1 presents the rate constants for the reactions of OH with each isomer of butanol in a single Arrhenius plot. The rate constants follow the order of n-butanol 154 CHAPTER 9. CONCLUDING REMARKS

(fastest), iso-butanol, sec-butanol, and tert-butanol (slowest). This is the same order that the ignition delay times for the isomers of butanol follow (with n-butanol having the shortest ignition delay time and tert-butanol having the longest ignition delay time) as found in shock tube experiments by Stranic et al. [35], supporting the notion that in a combustion reaction the reaction of OH with the oxidizing fuel is an important reaction pathway to ignition.

1250 K 1111 K 1000 K 909 K 833 K 10

] -1

s -1

molecules 3 (5.1) OH + n-Butanol cm OH + Butanol -> Products -11 (6.1) OH + iso-Butanol k (7.1) OH + sec-Butanol [10 (8.1) OH + tert-Butanol 0.1 0.8 0.9 1.0 1.1 1.2 1000/T [K-1]

Figure 9.1: Arrhenius plot of the rate constant determinations for Reactions (5.1), (6.1), (7.1), and (8.1) from the current work. The error bars represent the estimated uncertainty due to experimental and modeling uncertainties.

The rate constant determinations for Reactions (5.1), (6.1), (7.1), and (8.1) are sensitive to rate constants for secondary reactions related to decomposition of the respective butanol isomers. Thus, each rate constant provided by Eq. 5.2, Eq. 6.6, Eq. 7.1 and Eq. 8.12 has a diﬀerent level of uncertainty, as illustrated in Figure 9.1. In the current analysis, the best-known rate constants were ascribed to the important secondary OH-forming and OH-consuming reactions in the system to minimize the uncertainty in the overall rate constant. For the experiments investigating reactions with iso-butanol and tert-butanol, the kinetic parameters described by Eq. 6.4 and Eq. 8.8 were also determined, respectively, in addition to the 9.1. SUMMARY OF WORK 155

overall rate constant. ! 2, 350 knon-β = 1.84 × 10−10 exp − cm3molecule−1s−1 (Eq. 6.4) 6.1 T [K] ! 2435 k · (1 − br · br ) = 2.62 × 10−11 exp − cm3molecule−1s−1 8.1 OH β T [K] (Eq. 8.8)

These kinetic parameters approximately represent the rate of OH decay due to the reaction of OH with the respective butanol isomer, and the determined expressions were found to have reduced sensitivity to secondary rate constant parameters. The kinetic expressions given by Eq. 6.4 and Eq. 8.8 can be useful for validating high-level ab initio rate constant calculations, and also to validate and reﬁne detailed kinetic mechanisms describing the combustion of iso-butanol and tert-butanol, respectively.

The current high-temperature rate constant measurements can be combined with the data available in the literature reporting measurements of rate constant measurements at atmospheric-relevant conditions to generate empirical 3-parameter fits for the rate constants for Reactions (5.1), (6.1), (7.1), and (8.1) at intermediate temperatures. These three-parameter fits, expressed in a modified Arrhenius form, are given by Eq. 5.3, Eq. 6.7, Eq. 7.2, and Eq. 8.13.

! 1160 k = 1.78 × 10−21T 3.22 exp + cm3molecule−1s−1 (Eq. 5.3) 5.1 T [K] ! 1304 k = 1.65 × 10−21T 3.18 exp + cm3molecule−1s−1 (Eq. 6.7) 6.1 T [K] ! 1123 k = 4.95 × 10−20T 2.66 exp + cm3molecule−1s−1 (Eq. 7.2) 7.1 T [K] ! 450 k = 8.93 × 10−20T 2.60 exp + cm3molecule−1s−1 (Eq. 8.13) 8.1 T [K]

Eq. 5.3, Eq. 6.7, Eq. 7.2, and Eq. 8.13 are purely empirical relations that can be useful for interpolating rate constants at intermediate temperatures. 156 CHAPTER 9. CONCLUDING REMARKS

9.2 Implications for Addressing Global Challenges

The rate constants presented in this thesis for reactions of OH with n-alkanes and isomers of butanol succeed in extending the experimental database of high-temperature kinetic measurements for molecules relevant to transportation fuels. The results of this thesis can be applied to the improvement of detailed kinetic mechanisms describing the combustion of current practical and surrogate fuels (e.g. commercial gasoline, gasoline surrogates) and the next-generation biofuel (biobutanol). With the capability to create accurate detailed kinetic combustion mechanisms for transportation fuels, multi-scale combustion modeling capabilities can be improved and utilized to opti- mize the design and operation of advanced transportation engines burning evolving fuels, addressing our nation’s and world’s energy needs.

9.3 Recommendations for Future Work

9.3.1 Alkane Combustion Kinetics

The experimental techniques described in this thesis can be extended to the study

of high-temperature rate constants for reactions of OH with larger n-alkanes (≥C10) and branched alkanes to expand the experimental kinetic database for other alkane molecules important in the understanding of transportation fuels. n-Decane and n- dodecane are popular surrogates for diesel and jet fuels, respectively, and iso-octane is a primary reference fuel. Very few experimental studies have been reported in the literature regarding the rate constants for reactions of OH with these alkane molecules. The larger n-alkanes will have lower vapor pressures than the n-alkanes studied in this thesis, and therefore techniques for working with with low-vapor pressure fuels may need to be utilized, such as heating of the shock tube and gas-mixing facilities or use of an aerosol shock tube. These techniques should be compatible with the rate constant measurement methods developed in this thesis, though in experiments with low vapor pressure fuels, it is especially recommended that the laser absorption techniques described in this thesis, or other methods, be employed to verify initial 9.3. RECOMMENDATIONS FOR FUTURE WORK 157

fuel concentration. Furthermore, in experimental work with low vapor pressure compounds, there is a higher tendency for impurities to build up on the surfaces of the experimental facilities, and therefore the techniques for facility cleaning and impurity detection described in this thesis should be utilized. Experimental measurements of rate constants for larger n-alkanes and branched alkanes can be used to validate the extrapolation of structure-activity relationship methods to more types of alkanes, and these rate constant measurements can also lead to more accurate combustion mechanisms for various transportation fuels.

9.3.2 Butanol Combustion Kinetics

The studies carried out in this thesis on the reactions of OH with butanol have elucidated many areas relating to the high-temperature kinetics of the isomers of butanol. Future work including both experimental and theoretical studies on certain key reactions are recommended. In the current work, assumptions on the branching ratios of the reactions of OH with butanol were made in order to determine the overall rate constant. Improve- ments in the understanding of these branching ratios would be of great importance in advancing the understanding of biobutanol combustion. These branching ratios can be studied via theoretical or experimental means. For example, the works of Zhou et al. [88] and Zheng et al. [114] demonstrate the ability of ab initio methods to predict branching ratios for the OH plus butanol reactions for the n-butanol and iso-butanol isomers, respectively. These branching ratios can also be studied experimentally with the use of isotopic substitution. Deuterium substitution has been previously used by Carr et al. [135] and Tully and coworkers [129, 130] to determine branching ratios in reactions of OH with alcohols; however, deuterium-substituted alcohols can undergo ROD→ROH exchange, especially on stainless-steel surfaces, which introduces difficulties in knowing the actual fraction of deuterium-substituted alcohol in the experiments. Thus research efforts into methods for preventing this exchange or quantifying it would support efforts to measure the branching ratios of the OH 158 CHAPTER 9. CONCLUDING REMARKS

plus butanol reactions. Tully and coworkers also performed experiments with an 18O- labeled OH precursor; their experiments, however, were limited in temperature range and their highest temperature studied was near 750 K. Further research on using an 18O-labeled OH precursor for kinetic experiments near 1000 K is needed. Research using 18O-labeled alcohols for kinetic studies is also another avenue of isotopic labeling studies recommended for future work.

The reactions of the isomers of hydroxybutyl radicals are also important reaction pathways in the high-temperature kinetics of the isomers of butanol. Certain hydroxybutyl radicals have competing reaction pathways between an OH-producing channel and a non-OH-producing channel. These competing reactions can be beta-scission decomposition reactions or isomerization reactions. Because the formation and consumption of OH radicals is an important process in any combustion reaction, the competition between these decomposition channels of hydroxybutyl radicals is important. The works of Z´adorand Miller [93] and Zhang et al. [102] have demonstrated methods for calculating rate constants for beta-scission reactions of hydroxypropyl and 1-hydroxybutyl radicals, respectively, and can be extended to studies of all isomers of hydroxybutyl radicals. The experimental studies with isotopic labeling may also provide some insight on the relative rate constants for reactions of the isomers of hydroxybutyl radicals. With better understanding of the rate constants for reactions of hydroxybutyl radicals, important branching ratios of hydroxybutyl radical reactions can be determined.

The reaction of OH with tert-butanol is an especially good candidate to study using isotopic substitution. Only two reaction channels are present in this reaction, and the channel describing abstraction from the tert-butyl group is expected to lead to some OH regeneration. While the radical product after H-atom abstraction from the tert-butyl group, the hydroxybutyl radical (CH3)2(CH2)COH, is likely to decompose to form an OH radical, a non-OH-producing channel is also present. The branching ratios between these channels complicate the rate constant measurements carried out in this thesis. However, if either the oxygen or hydrogen atom in the alcohol group was labeled (with a 18O or D atom, respectively), then the OH regenerated 9.3. RECOMMENDATIONS FOR FUTURE WORK 159

after abstraction from the tert-butyl group does not interfere with the OH time- history measurement, and thus an overall rate constant can be directly measured with fewer interfering secondary reactions present. If the results are compared with the experiments presented in the current work (using the non-isotope-labeled tert- butanol), information about the important branching ratios can be determined. An example suggested future experiment is to repeat the experiments in Chapter 8 using 18O-labeled tert-butanol, and assume negligible kinetic isotope eﬀects. The OH sensitivity analysis will show sensitivity of OH only the overall rate constant for Reaction (8.1), and sensitivity to any branching ratios will be negligible. Therefore, the overall rate constant for Reaction (8.1) can be determined from the measured data. Because the product of k8.1 · (1 − brOH · brβ) has been determined in the current work and the branching ratio brOH can be estimated to a reasonable accuracy (see

Section 8.5), the branching ratio brβ can be determined by combining the results of the current work and new measurements using 18O-labeled tert-butanol. The type of measurement could yield the ﬁrst experimental study on the branching ratio brβ. The largest obstacle to completing this example experiment is ﬁnancial because 18O- 18 18 labeled compounds must be custom synthesized from H2 O, and H2 O is an expensive starting product. 160 CHAPTER 9. CONCLUDING REMARKS Appendix A

Shock Tube Cleaning Techniques

A.1 Introduction

This appendix outlines a method for characterizing the cleanliness of a shock tube, what to consider about impurities when running shock tube experiments, and various procedures for eliminating impurities. Sample case studies of shock tube cleaning anecdotes are presented, with all of the work being done on the Stanford Kinetics Shock Tube (KST) in the Mechanical Engineering Research Laboratory (MERL room 112) at Stanford University. These methods should be applicable on other shock tubes if the same assumptions and conclusions for appropriate cleaning methods for the KST also apply. Suggestions on improvements in shock tube design to minimize the eﬀect of impurities on experiments are also made.

A.2 Background

Shock tube experiments for studying chemical kinetics can be highly sensitive to impurities. For example, in ignition delay time studies of hydrogen combustion, hydrogen atom impurities initially in the shock tube can cause the chain branching reactions (i.e. H + O2 −→ OH + O) to occur sooner than when starting with pure

H2/O2 reactants. Additionally, kinetic rate constant measurements in shock tubes are typically performed with low levels of reactants on the order of tens to hundreds of

161 162 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES

ppm, such as the work described in this thesis, therefore, small ppm levels of impurities can compose a substantial fraction of the starting material in an experiment. Before designing a shock tube experiment, and during the analysis of data, it is important to understand the level of impurities in the shock tube and how the data may be aﬀected.

Impurities

Understanding the type(s) and origin of impurities that will have an effect on experiments will help one determine when one should be concerned about impurities in shock tube experiments. In the combustion process, the role of radicals is important, therefore, any artificial addition to the radical pool can have significant effect on kinetic experiments. Because shock tube experiments generally involve organic compounds (molecules containing carbon, and typically hydrogen), these molecules can condense and/or adsorb onto the shock tube facility surfaces, and remain even after long-term pumping of the facility using vacuum pumps. Compounds that are liquid at room temperature with low room temperature vapor pressures (on the order of tens of Torr or less) are more likely to “stick” to surfaces than compounds which are gas-phase at room temperature. Upon shock heating, hydrogen atoms, methyl radicals, and other alkyl fragments can separate from any molecules residing on the shock tube walls and react with the high-temperature gases.

Kinetics Shock Tube

The Stanford Kinetics Shock Tube is a stainless steel shock tube of 14.13 cm inner- diameter in both the 8.54-m long driven section and the 3.35-m long driver section. This facility is described in detail in Chapter 2 of this thesis. Typical experiments in this facility include ignition delay time measurements of gaseous and heavy hydrocarbon fuels (using on the order of a percent of fuel) and kinetic rate constant measurements (using on the order of tens to hundreds of ppm of fuel). Between experiments, the driven section is evacuated in two stages, ﬁrst with a roughing pump and then a turbo pump, and the driver section is evacuated with its own roughing A.3. IMPURITY CHARACTERIZATION 163

pump. Experimental measurements in the Kinetics Shock Tube are typically performed behind reﬂected shock waves at measurement ports located 2 cm from the endwall. The experimental mixtures are typically prepared in an internally-stirred 12-L stainless steel mixing tank through a mixing manifold with 14-port mixing manifold with 3/8” diameter stainless steel pipes before being introduced into the shock tube driven section through the mixing manifold at a location 5.74 m from the shock tube endwall. The mixing facility also has a two-stage evacuation procedure, with separate roughing and turbo pumps than the shock tube. A schematic of the mixing facility and the shock tube are shown in Figure A.1.

Not to scale

Mixing Tank Mixture fill Measurement port 5.74 m location 2 cm Diaphragm from endwall from endwall

Total driver section length = 8.54 m

Figure A.1: Schematic of the driven section of the Kinetics Shock Tube and gas-mixing facility.

A.3 Impurity Characterization

The purpose of cleaning the shock tube is to remove impurities, however, cleanliness is always relative. It means nothing to say a shock tube is clean if no proper baseline is set, and to set a baseline we must have a method to gage how clean a shock tube actually is. This section will outline a method to quantitatively determine the cleanliness of a shock tube, provide a case study of examining the cleanliness of the Kinetics Shock Tube, and then discuss how one might go about deciding what clean enough is. 164 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES

Previous Work

The thesis of J.T. Herbon [52] (on p. 77) notes that the identity and character of the shock tube impurities encountered are unknown, but were characterizable with

OH absorption. Herbon found in the Kinetics Shock Tube that “in 10% O2/Ar shock tube experiment after large hydrocarbon experiments and cleaning and vacuuming,

still ∼10 ppm OH formed at 1800 K equivalent to 8 ppm CH3. Flowing O2 directly into the shock tube reduced this to 1 ppm at 1700 K.” Herbon’s observations also included that impurities would accrue in the mixing tank as the residence time of the mixture increased. To reduce impurities in the mixing tank, a separate turbomolecular pump was installed for the mixing tank and mixing manifold and Herbon found that “using a new cleaner mixing assembly 100% O2 shocks at 1750 K give 2 ppm OH. At 10%

O2 yielded 0.8 ppm at 1850 K and 2 ppm at 2150 K.” Previous users of the shock tube facilities in the High-Temperature Gasdynamics Laboratory at Stanford University have used the same OH absorption technique to characterize the impurities in diﬀerent shock tubes. Their (unpublished) results are shown in Figure A.2. Impurities are present at higher levels at higher temperatures, likely due to increased reactivity of radicals with O2 or faster decomposition of the organic compounds “stuck” to the shock tube walls.

Procedure

OH absorption can be performed using a Spectra Physics 380 ring-dye cavity pumped with Rhodamine 6G dye and frequency doubled using an AD*A intra-cavity crystal (the same as the OH laser absorption system described in Chapter 2) to produce UV laser light around 306.7 nm, where OH absorbs strongly from the A-X (0,0) band. OH absorption measurements are typically performed at the experimental diagnostic ports 2 cm from the shock tube endwall, and it is assumed that all experiments shown in Figure A.2 are conducted there. A typical experiment involves ﬁlling the shock tube with a mixture of O2/Ar, tuning the laser to an absorption feature (i.e. R1(5) at 32606.54 cm−1), and measuring the absorption. Using absorption coeﬃcients from Herbon [52], the mole fraction of OH formed can be calculated, leading to an inference A.3. IMPURITY CHARACTERIZATION 165

of the amount of hydrogen atom impurities in the shock tube required to generate that amount of OH.

2500K 1250K 10 After Fuel HPST Petersen Experiments Kinetics Vasudevan Kinetics Herbon NASA Masten NASA Li 1

0.1 Incident Shock

Equivalent H-Atom Impurities [ppm] 0.01 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1000/T [1/K]

Figure A.2: Impurity measurement history in the shock tube facilities of the High-Temperature Gasdynamics Laboratory at Stanford University (unpublished). Data are shown for three diﬀerent shock tube facilities.

Case Study of a Contaminated Shock Tube

The cleanliness of the Kinetics Shock Tube facility was examined in the process of completing this thesis work. This work began after the shock tube was used for experimentation to study the ignition delay times of heavy organic fuels. It is believed that after the experiments, the shock tube driven section was cleaned with acetone- soaked cotton rags. While the source of the impurities cannot be uncovered, the locations where impurities are most deposited can be determined.

A commercial mixture of 2% O2/Ar, prepared by Praxair, was used to fill the shock tube from several different fill locations:

• Through the mixing manifold through an unused port and into the mixing tank where it was allowed to mix for at least 30 minutes (ﬁlled to ∼1 atm) before 166 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES

being introduced into the shock tube, again through the mixing manifold. • Through the mixing manifold through an unused port and directly into the shock tube, bypassing the mixing tank. • Directly to ports along the shock tube, completely bypassing the mixing manifold and mixing tank. Ports exist at 2 cm, 70 cm, 130 cm, 250 cm, 574 cm, and 814 cm from the driven section endwall.

Depending on where the O2/Ar mixture was introduced into the shock tube, different amount of OH were formed in experiments at similar temperatures. These experiments were repeated several times, indicating that these hot oxygen shocks did nothing to remove any impurities. Figure A.3 shows sample OH time-history measurements. OH is formed immediately after the reflected shock passing, and experiments which allowed the oxygen mixture to reside in the mixing tank produced the largest amount of OH, while filling from the mixing assembly also generated a significant amount of impurities.

OH time-histories in hot 2% O /Argon shocks around 2 1655 K for different fill locations in the shock tube

100

1 Endwall 1640 K OH mole fraction [ppm] Diaphragm 1668 K Mixing Manifold 1654 K Mixing Tank 1668 K 0123456 Time [ms]

Figure A.3: OH time-history measurements in hot 2% O2/Ar shocks near 1655 K for diﬀerent ﬁll locations in the shock tube. “Endwall” is a port 2 cm from the driven section endwall, “diaphragm” is a port 814 cm from the endwall, “mixing assembly” is through the manifold bypassing the mixing tank, and mixing tank is from the mixing tank after a 30 minute residence.

From these results, it can be concluded that the mixing tank and mixing assembly are a major source of impurities. The shock tube, however, is also a major contributor A.3. IMPURITY CHARACTERIZATION 167

to impurities, which can be seen in the experiments where the oxygen mixture is filled directly into the shock tube at ports along the driven section. Figure A.4 shows the peak OH mole fractions formed as a function of the fill location. The largest impurities were observed to form when the oxygen mixture was filled furthest from the endwall, and no impurities were visible when the oxygen mixture was filled at the diagnostic location at the endwall. This indicates that a gaseous mixture introduced into the shock tube will entrain any impurities as it propagates to the endwall. Therefore, when cleaning the shock tube, the entire section between the filling location and the measurement location must be cleaned, and it is not enough to just clean the measurement location.

Endwall Diaphragm

100

Filled directly into shock tube Fill through the mixing assembly

Equivalent H-Atom Impurities [ppm] Fill through the mixing tank 1 012345678 Distance from the endwall [meters]

Figure A.4: Peak OH mole fraction formed in hot 2% O2/Ar shocks around 1655 K as a function of ﬁll location.

These experiments were done at several temperatures and shown in Figure A.5 compared with the previous measurements in the kinetics shock tube, and it is obvious that the shock tube is very dirty at this point. Figure A.5 also shows measurements done after attempted cleaning of the shock tube by “baking” the shock tube at 60 ◦C and using a turbomolecular pump to remove impurities. This method is shown to be ineﬀective since the level of measured impurities after the “baking” does not change. 168 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES

Amount of OH observed in hot shocks of 2% O in Argon 2

2500K 1667 K 1250 K 1000 K 1000 Previous Measurements (Assumed filled from endwall) Mixing tank Vasudevan Herbon 100 Diaphragm Current Measurements Mixing manifold (Before heated pumping) Mix manifold location Fill from diaphragm 10 Fill through mixing tank Fill through mixing manifold Fill from endwall Current measurements 1 (After 5 days of pumping Endwall a heated shock tube) Fill from diaphragm Fill from mixing manifold 0.1 Fill from 2.5 m from endwall Fill form 70 cm from endwall Equivalent H-Atom Impurities [ppm] Vasudevan/Herbon Fill from 130 cm from endwall Fill from endwall 0.01 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1000/T [1/K]

Figure A.5: Peak OH mole fraction formed in hot 2% O2/Ar shocks at various temperatures and diﬀerent ﬁll locations and compared to previously taken data (unpublished).

This case study illustrates several important principles. First, the shock tube facilities can get very dirty after months of ignition delay time experiments, even after some cleaning is done. Even if the shock tube driven section is thought to have been cleaned by “washing” with acetone-soaked rags, impurities can still exist. Second, for high-temperature experiments in excess of 1500 K, up to 100 ppm of equivalent H atoms originating from the facility surfaces can be present, which can have a large impact on kinetic rate constant measurements. Impurities do have a smaller impact at lower temperatures, however, so even at temperatures less than 1000 K, one should expect no more than ∼10 ppm of equivalent H atoms regardless of the shock tube cleanliness state (at least if the assumption is made that the state for this case study was “as dirty as a shock tube will get”). Third, because gas mixtures can entrain impurities from contaminated surfaces, shock tube experiments with mixtures introduced at the measurement location (in this case the endwall) would eliminate the need to clean the entirety of the driven section. A.3. IMPURITY CHARACTERIZATION 169

Modeling Impurities

In the previous section, it was found that up to 100 ppm of equivalent H-atoms in the shock tube can be present, though as low as a few ppm have been previously detected. The next question one might ask after finding out the level of impurities in the shock tube is what to do about the impurities. If 100 ppm of impurities has no noticeable effect on the experiments that are to be conducted, then spending time cleaning the facility is just an exercise in compulsivity.1 To determine whether the amount of impurities found in the shock tube have significant effect, detailed kinetic mechanisms can be used. Many kinetic experiments performed are compared with kinetic mechanisms, so it is likely a mechanism is already available describing the kinetic system of interest. If not, a kinetic mechanism for a similar fuel can be used. Because the source of the impurities is unknown, modeling them is not entirely straightforward. Two simple options exist: 1. model the impurities as H atoms, and run kinetic calculations with the planned experimental conditions, but with a starting concentration of H atoms equal to the equivalent H-atom impurities measured, or 2. because the impurities may also come from hydrocarbon fragments which can fall apart during shock heating, modeling the impurities as methyl radicals may also be appropriate. In this case, run kinetic calculation with the planned experimental conditions, but with a starting concentration of CH3 equal to the equivalent H-atom impurities measured divided by three. Larger hydrocarbon fragments can also be considered in a similar manner. If both simulations yield negligible effects on the desired result quantity of interest (as compared to the simulations without any impurities in the initial composition), then cleaning the shock tube may be unnecessary. If the calculations of the data you are studying are sensitive to either form of impurities, cleaning the shock tube is a good option. It should be noted, though, that kinetic mechanisms may not always be accurate, and impurities can have a larger effect if the radical chemistry in the

1That said, however, this is only true if you uncover the impurities during your experimental run. Proper lab equipment sharing etiquette would require you to clean up the facility after yourself for the next user, regardless of what their experiments are, or whose experiments deposited the impurities on the facility to begin with 170 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES

kinetic mechanism is in error. Therefore, always use proper judgment of the analysis tool when making experimental decisions.

Notes on Characterizing Impurities

Using the OH laser to characterize the amount of impurities in the shock tube facility, and examining where the majority of the impurities are, can be a very useful tool in determine whether to and where to clean your shock tube. After cleaning the shock tube, one should always re-characterize the impurity level to verify that the cleaning was successful. If modeling indicated that less than 1 ppm of equivalent H-atom impurities is needed for eliminating experimental sensitivity to impurities, then a more sensitive diagnostic than the Spectra Physics cavity used for OH measurements is necessary. While characterizing the impurities is useful, it may not always be practical, for example if the diagnostic is not set up, or if the researcher is not familiar with the operation of the OH laser. In this case, all parts of the shock tube facility should be cleaned frequently during experiments, and level of impurities can be estimated based on past work.

A.4 Gas-mixing Facility Cleaning Methods

Because the mixing tank and mixing manifold can be a large source of impurities, learning methods to clean them is essential. This section will discuss two diﬀerent methods of cleaning these. All examples discussed refer to data taken on the Kinetics Shock Tube Facility.

Brute Force Disassembly for Cleaning

As described in Chapter 2, the mixing manifold is constructed with a central welded piece of cross pipe of 3/8” diameter, and connected to various sources via Swagelok stainless steel 8BK bellow valves which use PCTFE (Polychlorotriﬂuoroethylene) A.4. GAS-MIXING FACILITY CLEANING METHODS 171

stem tips. Ultra-Torr fittings were used in connecting the values with the liquid chemical components. Brute force cleaning of the mixing assembly can be completed by removing all the valves, thereby freeing the center piece of cross pipe to be cleaned as well. Each valve can be disassembled into the valve body and the bellow section, so that the stem tips and gaskets can be replaced. Each valve body can be cleaned using acetone-soaked cotton swabs until no color residue comes off onto the swabs when used to abrasively rub the valve surface. For components that are excessively dirty, they can be sent to be professionally cleaned, or replacement parts can be purchased. The miscellaneous parts, such as the Ultra-Torr fittings, and minor piping to other components, can also be cleaned with acetone-soaked cotton swabs. New stem tips can be installed after cleaning of the valve components. The mixing tank can be disconnected from the manifold and disassembled. The stainless steel body and brass mixing vanes can be cleaned by using a solvent such as acetone, and scrubbing with cotton or cheesecloth rags. The mixing vanes can be disassembled and the joints cleaned. If the interior of the mixing tank looks especially dirty, a professionally done electro-polish may be necessary. Prior to the work presented in this thesis, the mixing tank body and mixing vanes were professionally electro-polished. The above procedure described the cleaning done on the mixing facility immediately before the start of the experiments presented in this thesis.

Chemical Cleaning

The brute force cleaning of the mixing assembly is very thorough, and allows all the cracks and crevices in the assembly to be cleaned. However, that method requires disassembly of the entire mixing assembly, which is not always practical, especially when chemicals frequently remain on the facility surfaces after only a few experiments. After brute force disassembly and professional cleaning in the brute force method, all impurities were eliminated from the mixing tank and manifold, however, after making one mixture 1% n-nonane and argon, over 100 ppm of equivalent H-atom impurities 172 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES

were found in the mixing tank, as illustrated by the measured OH time-histories in Figure A.6. A simpler method of cleaning the mixing facility involves ﬂushing with peroxide chemicals, and does not require any disassembly of the mixing facility. Before describing the procedure, Figure A.6 shows evidence for this working.

2% O /Ar shocks, filled from mixing tank after residence for ~ 1 hour 2 300 300 300 Measurement after Measurement after Measurement after professional cleaning making one mixture "flushing" with TBHP 250 of mixing facility 250 in the "clean" mixing 250 method (1382 K) components in the brute facility (1368 K) force disassembly 200 method (1350 K) 200 200

150 150 150

100 100 100

50 50 50 OH mole fraction [ppm] 0 0 0

-101234-101234-101234 Time [100 s]

Figure A.6: OH time-histories measured in 2% O2/Ar shocks, ﬁlled into the shock tube from the mixing facility after residence in the mixing tank for ∼1 hour, illustrating that preparing mixtures can quickly contaminate the mixing assembly, and “ﬂushing” with TBHP can improve the cleanliness.

tert-Butylhydroperoxide (TBHP) is used as the peroxide for cleaning, largely because it is also the OH precursor used for the kinetic experiments in this thesis and is easily available and easy to handle. TBHP decomposes into OH, methyl, and acetone (see Figure 3.1), and decomposition rates have been studied in Chapter 3. Upon decomposition, the radicals can react with any organic molecules adhering to the facility walls, and either water or methane gas will form that can be evacuated from the facility, removing hydrogen-containing impurities. The procedure for “ﬂushing” with the TBHP solution2 in the Kinetics Shock Tube which was found to remove impurities is as follows:

2In this case, reference to the TBHP solution will refer to the commercially available solution of 70%, by weight, TBHP in water from Sigma Aldrich, the same chemical described in Chapter 2 of this thesis. A.5. SHOCK TUBE CLEANING METHODS 173

1. Heat the mixing tank and mixing manifold to 50 ◦C and isolate them from the shock tube. 2. Place some amount of the TBHP solution in a glass storage vessel and attach to the shock tube and attach it to a liquid fuel connector on the mixing manifold. 3. Use the mixing facility roughing pump to pump out the air in the glass vessel. (not all of the air must be removed, just the majority of the vapor should be from the TBHP solution). 4. Introduce approximately 7 to 14 Torr of the TBHP solution vapor into the mixing tank and manifold. 5. Let sit and react overnight. 6. Pump out the TBHP solution vapor and any reacted products using the two- step roughing and turbo pump procedure for the mixing facility. Overnight pumping is recommended.

This procedure was the one followed to eliminate the impurities shown in Figure A.6. While this cleaning procedure is simpler than disassembling the mixing assembly, it is still a two-day process. The necessity of allowing the TBHP solution vapors to sit and react overnight has not been scientifically proven, however, two hours of reacting has been shown to be ineffective. Since water is likely formed in reactions during “flushing,” a long pump out time is recommended.

A.5 Shock Tube Cleaning Methods

Because the shock tube was also shown to be a possible large contributor to hosting impurities, methods for cleaning the shock tube itself must be examined. Several methods for cleaning the shock tube exist, some being highly eﬀective, some are myths, and some have not yet been tested. 174 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES

Cleaning Myths

Myth 1: Shock Tube Baking

Several research publications, including Herbon [52], have suggested baking the shock tube and pumping on it overnight would drive any impurity residue oﬀ of the walls. In Section A.3, experiments were performed that illustrate this to not be eﬀective.

Myth 2: Cotton Rags

Researchers in the High Temperature Gasdynamics Laboratory at Stanford University have, in the past, used the procedure of passing acetone-soaked cotton t-shirt rags through the shock tube, using a plunger-like device with a slightly larger diameter than the shock tube as the main cleaning method of the shock tubes. This was done after ignition delay time experiments with heavy hydrocarbon fuels, and the impurities remaining in the shock tube were characterized in Section A.3. This was found to be largely ineﬀective, likely because the cotton rags are not very absorbent; therefore, not a lot of solvent will be present on them during this type of cleaning, and larger scrubbing forces would be required to remove any residue stuck to the surfaces. After using a plunger device to pass acetone-soaked cotton rags through the Kinetics Shock Tube, the cleanliness of the shock tube was tested by scrubbing the interior of the shock tube with more acetone-soaked cotton rags by hand using larger scrubbing forces (at the endwall and at the shock tube interior done by taking apart the shock tube segments) and it was found that residue still came oﬀ of the walls. Therefore, this cleaning technique will only work if larger scrubbing forces can be applied (i.e. larger diameter plunger) or more solvent can be placed on the rags. A similar yet superior cleaning technique is presented in the following subsection.

Solvent Cleaning with Cheesecloth Rags

Cheesecloth rags are many times more absorbent than cotton t-shirt rags. A test of comparing the eﬀectiveness of cleaning using an acetone-soaked cheesecloth rag with an acetone-soaked t-shirt rag was performed by trying to clean old permanent A.5. SHOCK TUBE CLEANING METHODS 175

marker writings from the optical tables. Using the acetone-soaked cotton rag, large amounts of force were required to scrub the permanent marker clean, however, using the cheesecloth rag soaked with acetone, only a feather-light wiping action was needed because of the much larger amount of acetone released onto the surface upon contact. Therefore, the acetone-soaked-cheesecloth-on-a-plunger technique for cleaning the shock tube interior should be a superior technique to the cotton t-shirt rags.

Brute Force Disassembly for Cleaning

For a more thorough cleaning of the shock tube, all the divisions can be disassembled, and the crevices cleaned. In this process, the o-ring and o-ring grooves can also be replaced or cleaned. This process is recommended to be done periodically, and for the Kinetics Shock Tube, takes approximately one to two weeks to complete. The next paragraph of this subsection will report the brute force cleaning procedure used prior to the start of the experiments conducted in this thesis. The shock tube driver section is composed of two sections. The end cap of the driver section was removed, and the section cleaned with acetone-soaked-cheesecloth- on-a-plunger technique until the rags came out clean. The shock tube driven section is composed of six pieces of large steel tube, of where each piece, except the two nearest the endwall, is supported by two rollers and can traverse axially and rest independently without being attached to another piece. The piece second closest to the endwall is bolted to a concrete slab attached to the ground, and the endwall section is removable entirely. The endwall section was unbolted first. The section is heavy, requiring two average people to lift it. All the plugs were removed and cleaned. Because the entire end section was fully removable and mobile, it was sent to be professionally electro-polished. The unbolting of the rest of the driven section had to begin at the diaphragm end because of where the shock tube was affixed to the ground. The first section was unbolted. To create a larger space to separate the sections to clean between, the diaphragm end section was raised such that the side plug would not contact the end support. The tee-section was removed before proceeding to the next section. The mechanical pumps were detached from the tee 176 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES

section, as was the cooling fan of the turbo pump, and all other components that were attached via a Kwik-ﬂange ﬁtting. The tee section was supported on a rolling cart before being unbolted. This allowed for easy movement of the tee section after unbolting. The rod seat was used to pull out the valve seat. All accessible areas of the tee section were cleaned, and all the o-rings of the tee section replaced. The last section of the shock tube was unbolted, cleaned, placed with a new o-ring, and then bolted back together. All the shock tube sections and tee section were then bolted back together. After unbolting and cleaning all the shock tube sections, all the plugs were removed and cleaned, and the o-rings replaced. The unbolting and cleaning of the entire shock tube took a fully dedicated six days (approximately 40 hours), with more than two people working only on three of these days.

Untested Methods

Untested Method 1: Chemical Cleaning

The “flushing” method with the TBHP solution in theory should also work for the shock tube, however, has not been tested to the author’s knowledge. However, when extending the flushing method to the shock tube, one must take into consideration that most shock tubes are not heated, and the reactions that contribute to the cleaning of impurities during “flushing” are temperature dependent (and recall in the TBHP “flushing” procedure the mixing assembly was heated to 50 ◦C). If the shock tube is at room temperature, expect the cleaning process to occur more slowly because the decomposition rate of TBHP is four orders of magnitude slower at room temperature than at 50 ◦C (recall this rate constant was measured in Chapter 3, see Figure 3.7 for the results). If attempting to use TBHP “flushing” to clean the shock tube, it is recommended that the shock tube walls are heated or the time intervals in the procedure be extended. A.6. ADDITIONAL COMMENTS 177

Untested Method 2: Non-hydrogen Containing Solvent

If cleaning using a solvent, one might be concerned with using a hydrogen-based solvent because it might introduce more hydrogen into the shock tube. Trichlorotri- ﬂuoroethane is a non-hydrogen containing solvent, which has been shown to be stable on stainless steel surfaces [136], and is an alternative for solvent cleaning.

A.6 Additional Comments

This appendix only covers shock tube cleaning to remove impurities. Proper maintenance of the shock tube facilities include frequent cleaning and leak checks. The leak checks should be performed after any brute force disassembly for cleaning. Mainte- nance suggested by the manufacturer’s manuals for the pumps and other equipment is also recommended. Because impurities have been shown to build up in the shock tube facilities over time, experimentalists should periodically check to ensure that their facilities are clean. To keep track of what might be the causes of impurities, keeping an experimental and maintenance log record is recommended, including information on the date of experiments, chemical used, number of shocks, diaphragm thickness, cleaning history, pump maintenance record, etc. 178 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES Appendix B

Microwave Discharge System

B.1 Introduction

Improper alignment of the Burleigh WA-1000 visible wavemeter was found to lead to errors of up to 0.05 cm−1 in the visible laser wavelength measurement. This was discovered by using a Bristol 621 wavemeter to simultaneously measure the laser wavelength. To check the accuracy of the wavelength measurements from these wavemeters and further reduce concerns about errors in the wavelength measurement, a microwave discharge of He/H2O was used to generate OH radicals; the absorption line center position is known for OH, thereby allowing conﬁrmation of the measured wavelength.

B.2 Equipment Setup and Procedure

An Opthos MPG-4 microwave generator was used with an Evenson cavity for this experimental setup. An H2O saturator was created with an Erlenmeyer flask and a 2-hole rubber stopper with 1/4” stainless-steel piping entering and exiting, and Swagelok ball valves were also used. Figure B.1 shows a schematic of the microwave discharge cell setup with an H2O saturator used for generating a pool of OH radicals. The UV laser beam was split off from the laser setup described in Chapter 2 (see Figure 2.4) using a UV-grade beam splitter and passed through the discharge cavity. In-house modified PDA36A detectors were used to monitor both the incident and

179 180 APPENDIX B. MICROWAVE DISCHARGE SYSTEM

transmitted light intensities as the laser was tuned over the OH lineshape while the visible laser wavelength was monitored with the Burleigh WA-1000 visible wavemeter. The following procedure was used for in the operation of the microwave discharge cell and H2O saturator:

1. Turn on the pump. 2. Turn the power control all the way counter clockwise on the Opthos MPG-4 microwave generator and turn on the power. 3. Open the valve (1) to the cooling air coming from the building compressed air lines.

4. Check to make sure the valves (3,4) connecting the H2O saturator are closed, and the through line valve (2) for helium is open. 5. Open the helium regulator and valves (5) such that you begin ﬂowing pure helium through the cell so that the Baratron reads 6 Torr. 6. After at least 3 minutes past turning on the microwave generator, turn on the High Voltage switch on the generator. 7. Increase the power control until approximately 50 W appears on the forward power. 8. Use a Tesla coil to start the discharge. 9. Once the discharge has started, adjust the threaded tuning stub projecting into the Evenson cavity (a) and the three part tuning handle that slides along the center conductor (b) until the reverse power is minimized.

10. Slowly open the valve (4) to the H2O saturator and valve (5) allowing helium to ﬂow into the saturator without allowing the pressure to increase too much. This may involve closing the valve (2) for the helium through line.

To shut oﬀ:

1. Turn oﬀ the microwave power generator. 2. Close the valve (1) for the cooling air. 3. Close the valve (5) and the regulator for the helium. B.3. RESULTS 181

Building Compressed Air

Microwave Power (1) Supply Cooling air

(b) UV beam

(a) Microwave discharge cavity 1000 Torr Baratron

(2) Pump

(3) (5)

Helium gas

(4)

H2O saturator

Figure B.1: Schematic of He/H O microwave discharge cell and H O saturator setup. Figure adapted 2 2 from Herbon [52]. Figure modified from John Herbon’s thesis

B.3 Results

The microwave discharge cell was run at a pressure of ∼1 Torr and with a net power of 30 Watts to the cavity. The wavelength of the UV laser was tuned using the in-cavity etalon over the R1(4) and R1(5) lines in the A–X (0,0) band of the OH absorption spectrum, and the transmission of the UV laser through the discharge cell recorded with an uncertainty of 4%. The expected line shapes are calculated using the work of Herbon [52], and compared with the measured UV transmission data in Figure B.2. The peaks of the experimental transmission matched the line centers within 0.003 cm−1, which is well within the resolution and uncertainty limits of the wavemeter. This agreement in wavelength of the line center was only found when the wavemeter was aligned properly according to the manufacturer’s speciﬁcations 182 APPENDIX B. MICROWAVE DISCHARGE SYSTEM

(“the tracer beam and input laser beam must be precisely collinear over a one meter path from the Wavemeter input aperture within 1.5 mm”). A fiber-coupled input to the Burleigh WA-1000 was also tested, and this setup also yielded results that indicated correct wavelength measurements. The fiber-coupled input was also easier to ensure proper alignment, because any improper alignment through the fiber would not produce a measurement reading on the wavemeter.

Measured transmission through OH in the He/H O cell 2

OH lineshape at 298 K, 1 Torr

1.0 1.0 Transmission 0.8 0.8 R (4) line 1 R (5) line 0.6 0.6 1

0.4 0.4

0.2 0.2

0.0 -1 0.0 line center 16296.555 cm line center 16303.275 cm-1 16296.4 16296.5 16296.6 16296.7 16303.1 16303.2 16303.3 16303.4

-1 Absorption Croefficient [Arbitrary units] / Wavenumbers (vis) [cm ]

Figure B.2: OH line shapes, calculated and measured.

At 298 K, the full width at half maximum (FWHM) of the line shape is 0.1 cm−1. In the pre-frequency doubled visible beam which is being monitored by the wavemeter, that line center becomes 16303.22775 cm−1, and the FWHM becomes 0.05 cm−1. The FWHM of the line shape is consistent with what would be found assuming only Doppler broadening exists at this low pressure (at 298 K). Because the discharge cell was operated at low pressures, minimal pressure broadening can be assumed and a Doppler line shape can be ﬁt to the data. Figure B.3 shows this, using Eq. B.1 to ﬁt the measured line shape.

!1/2 2kT ∆ν = 2(ln 2)1/2ν = 0.098cm−1 (Eq. B.1) Doppler 0 mc2 B.4. CONCLUSIONS 183

From these results, we can deduce a temperature of approximately 800 K, which is reasonable considering much of the 100 W of forward power coming from the microwave power supply must go towards increasing the translational temperature of the gas.

OH absorption data in the He/H O cell 2 Doppler profilie fit using experimental line width (T=800 K) 100

[%] -100 Residual 20

15 R (5) line 1 10

5 [Arbitrary units] 0

OH Absorption Coefficient 16303.2 16303.3 16303.4 Wavenumber (visible) [cm-1]

Figure B.3: Measured OH line shape compared with the Doppler proﬁle ﬁt at a temperature of 800 K.

B.4 Conclusions

In this process of examining how the wavelength is measured using the Burleigh WA- 1000 visible wavemeter, it was learned that the wavemeter reading can be sensitive to alignment, especially when not following the speciﬁcations required for alignment as stated in the manual. Using the ﬁber-coupled input provides a more robust alignment, and should be preferred, but is not necessary if the proper alignment procedure is followed for freespace alignment. By using a microwave discharge source to generate

OH atoms in a He/H2O mixture, it was concluded that the wavemeter measurement using the freespace alignment is accurate when aligned properly. 184 APPENDIX B. MICROWAVE DISCHARGE SYSTEM

The proper use of the Burleigh WA-1000 wavemeter should always involve the following procedures:

• Aligning the tracer beam from the Wavemeter free-space aperture to the incoming laser beam over a path length of > 1 m to be separated by no more than 1.5 mm. • Because the incoming laser beam and the tracer beam have ﬁnite diameters, placing an iris both at the dye laser cavity exit and near the Wavemeter entrance can help facilitate ensuring the laser beams are aligned. Because the Wavemeter entrance is in itself an aperture, and iris at this location is not as critical. • The alignment must be checked every time the optics in the laser dye cavity are adjusted. Appendix C

Fuel Measurement using a Helium-neon Laser

C.1 Introduction

Light absorption at a wavelength of 3.39 µm occurs due to excitation of the C–H stretch vibrational mode, and thus the mole fraction of any hydrocarbon species can be determined using the Beer-Lambert law, given by Eq. 2.1, if the absorption cross- section for the chemical of interest at 3.39 µm is known. This appendix describes the utilization of laser absorption at 3.39 µm to determine the mixing time required for the mixture preparation process and to verify the composition of the double-dilution- prepared mixtures.

C.2 Equipment

An infra-red Jodon Helium-Neon laser (HeNe, Model HN-10GIR) of wavelength 3.39 µm was utilized to generate laser light at 3.39 µm. The intensity of the HeNe laser light was measured using liquid-nitrogen-cooled indium antimonide (InSb) detectors from IR Associates (model no. IS-2.0). Miscellaneous optics were used in the alignment of the laser light, all compatible with transmitting, reﬂecting, ﬁltering, and splitting of laser light at 3.39 µm. This laser light was passed into a cell containing

185 186 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER

the absorbing gas; both the shock tube described in Chapter 2 of this thesis and a Toptica Photonics model no. CMP30 multi-pass cell of total path length 30 m were utilized as absorption cells.

C.3 Mixing Time Determination

Several mixtures of approximately 0.3% n-heptane in argon were prepared in the gas- mixing facility described in Chapter 2, each in one single-dilution step, to determine the mixing time required in the mixture preparation process to ensure homogeneity and consistency. Each mixture was allowed to mix for different initial amounts of time before being filled into the shock tube to a pressure of 100 Torr. The HeNe laser was passed through the shock tube at the windows 2 cm from the driven section endwall to measure the composition of n-heptane in the mixture. The optical setup was similar to the setup for the OH diagnostic system shown in Figure 2.4, except with the HeNe laser, InSb detectors, IR beam splitter, and 3.39 µm bandpass filters in place of the OH laser system, modified PDA36A detectors, UG-grade beam splitter, and UG11 filters, respectively. Common-mode rejection was employed, and the measured transmission was averaged over several seconds. An absorption cross-section for n- heptane from Klingbeil et al. [53] was used in determining n-heptane mole fraction from the Beer-Lambert law given by Eq. 2.1. From these experiments, it was determined that the mole fraction of n-heptane in the gas mixture reached a homogeneous mixture of the expected composition after approximately 30 minutes. A plot of the measured n-heptane mole fraction versus mixing time is shown in Figure C.1. The experiments described in this thesis used a mixing time of greater than or equal to 45 minutes for each mixing step of all mixtures. It should be noted that even after 45 minutes in the mixing tank, a small portion of the gas mixture near the exit valve remains unmixed (between the mixing tank and the closest valve to the mixing tank; see Figure 2.3), and this portion of the gas mixture must be vented out through the manifold prior to use of the mixture. C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 187

0.4

0.3

0.2

0.1 -heptane concentration [%] n

0.0 0 102030405060 Mixing time [minutes]

Figure C.1: Measured n-heptane mole fractions of a n-heptane/argon mixture after being ﬁlled into the shock tube after diﬀerent mixing times.

C.4 Mole Fraction Measurements in a Multi-pass Cell

The test mixtures prepared for the experimental work presented in this thesis are composed of highly dilute (ppm levels) of organic compounds. Uncertainties in the rate constant determinations are almost 1:1 proportional to the uncertainty in the known initial fuel composition in the test mixtures. Because the fuels of interest in this thesis are all liquid at room temperature, concerns about fuel condensation and/or adsorption onto the facility wall surfaces are present, and these effects can lead to lower initial fuel compositions than would be predicted according to the manometrically prepared predictions. Therefore, efforts were placed into developing a method for experimental confirmation of the composition of the prepared mixture. Because of the ultra-low concentrations of absorbing species in the mixtures, typical laser absorption techniques for quantitative mole fraction measurements can be difficult because of low absorption fractions. To address this problem, a 74-pass, 30 m multi-pass absorption cell was set up to perform fuel mole fraction measurements at 188 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER

3.39 µm; the details of the cell are as follows:

• Toptica Photonics CMP30 Multi-pass absorption cell • Total path length = 29.87 m (74 passes) • Total transmission (excluding window) ≥26%

• Mirrors are BK7, windows are CaF2, all work with 3.39 microns

Alignment Procedure

The cell alignment is straight forward. According to the manufacturer’s instructions, two alignment cards come with the cell, and are to be placed along the holes on the optical table that the cell is to be bolted into. The alignment cards each have a target, and the cell is aligned by aligning the laser through the target holes on the alignment cards, and then removing the cards and bolting the cell in at the location of the cards. This is easily done with a visible helium-neon laser. See Figure C.2 for a photo of the alignment card set up. The alignment can be checked by counting 36 reﬂections on the inner mirror of the cell. Alignment of an infra-red (IR) helium-neon laser into the multi-pass cell is more diﬃcult because of the inability to see the IR laser beam and check its alignment through the cards. The following procedure was developed to align the IR laser beam through the multi-pass cell by making use of a visible helium-neon laser; Figure C.3 shows a schematic of the optical setup.

1. Direct the IR HeNe laser beam to reflect off of M1 and arrive on M2. Temperature-sensitive paper cards can facilitate this. 2. Place irises at two locations in the beam path between M1 and M2, such that the IR beam passes through both. 3. Raise the flipper mirror for the visible HeNe, and align that mirror and the visible HeNe such that the visible beam passes through both irises. 4. Use the visible beam to place M3 and M4 in approximate locations such that the visible beam is directed through the multi-pass cell. 5. Place a suitable long focal length spherical lens between M2 and M3 such that the laser light is focused at the center of the multi-pass cell. C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 189

Manufacturer supplied alignment cards Alignment cards with large window holes for IR laser alignment

Alignment mirror Mx Detector

Figure C.2: Alignment card setup for the multi-pass cell using the manufacturer supplied cards (left). Also shown are the alignment cards duplicated with large window holes for alignment of the IR laser beam (right).

aser flipper eNe L n IR H mirror Jodo

Visible HeNe

Iris 1 M1 Iris 1 M2 M3 Lens InSb InSb Detector M4 Detector

Multi-pass Cell

Mx InSb Detector

Figure C.3: Multi-pass cell setup with HeNe laser. 190 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER

6. Adjust M3 and M4 as necessary to follow the alignment procedures detailed in the multi-pass cell instruction manual using the provided alignment cards. 7. Place the multi-pass cell in place, and observe the laser light coming out of the cell (Note that you will see two beams exiting from the cell window: one is the reflected beam from the window, and the other is the transmitted light. Examination of the reflection geometry will tell you which is which). 8. Place a short focal length lens or focusing mirror in the transmitted beam path, and a suitable IR detector (e.g. a liquid-nitrogen-cooled InSb detector) at the focal point of the lens/mirror. 9. Un-flip the flipper mirror for the visible HeNe to allow the IR laser light to pass, and remove the irises to ensure that none of the laser beam is cut off. 10. If you now see a voltage on the IR detector, the alignment is complete and the subsequent steps can be skipped.

If no IR beam is detected, this means that the visible and IR laser beams were not perfectly aligned to be co-linear using the irises. This is not a problem. The following additional steps were developed to ﬁne tune the alignment of the IR laser into the multi-pass cell.

11. Remove the multi-pass cell from the table and put the alignment cards back in place, but with large window holes centered at the points where the laser beam should pass through (see Figure C.2). Duplicates of the alignment cards are suggested to be made as to not cut holes in the original manufacturer supplied alignment cards. 12. Place a focusing mirror or lens where the laser beam would exit the alignment cards (Mx). This can be facilitated by raising the ﬂipper mirror for the visible HeNe and aligning Mx with the visible laser light. 13. Place another IR detector at the focal point of the focusing optic (see Fig- ure C.2), and align the detector such that it detects the IR laser beam, and that the laser beam hits the center of the detector’s active area. Note that the IR laser beam may hit the detector at a slightly diﬀerent location than the visible laser beam because the two may not be exactly co-linear. C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 191

14. If desired, use this opportunity to check that the IR laser beam is not clipped on any of the optics by using a knife edge (or business cards) to locate the position of the IR laser beam at all important locations. The measured laser intensity of the newly set up detector should fall once the knife edge has clipped one edge of the laser beam. 15. Use a knife edge to locate the position of the IR laser beam at the location of the alignment cards, and adjust M3 and M4 until the IR beam is aligned properly, through the center of the holes in the alignment cards. 16. Once alignment is veriﬁed, put the multi-pass cell back in place. If the previous step was done carefully, the IR detector should now detect the transmitted beam. If it still does not, repeat the above steps carefully until alignment is achieved. 17. As an alternate solution to the above steps, if temperature-sensitive paper cards are able to detect the position of the IR laser beam at the position of the multi- pass cell, these can be used to check whether the IR beam is aligned correctly through the alignment tools provided by the multi-pass cell manufacturer. The above steps are only necessary if the IR laser intensity has attenuated enough that the temperature-sensitive paper cards available can not detect the laser beam location (as was the case for the Jodon HeNe laser).

If common-mode rejection is desired, follow the following steps.

18. Raise the flipper mirror for the visible HeNe such that the visible laser is aligned into the multi-pass cell. 19. Locate the reflected beam from the window of the cell, and align the reflected light into a focusing optic and a suitable IR detector. 20. Lower the flipper mirror. The IR detector should detect the reflected IR laser light from the cell window and this signal can be used for common-mode rejection.

It should be noted that the above procedure only explains how to provide a successful alignment of the cell. Additional steps were performed to check the beam diameter at the cell window entrance, cell center, and rear cell mirror using an InSb detector and 192 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER

a vertical slit; to determine the beam diameter at a particular position, the vertical slit was used to determine when the slit width spanned exactly the laser diameter. The multi-pass cell setup was connected to the mixing manifold of the shock tube to make absorption measurements for low-concentration prepared mixtures. One end of the multi-pass cell is connected to the mixing manifold to allow the mixture to ﬂow in, and the other end of the cell is connected to the vacuum pumps of the mixing facility, a 1000 Torr Baratron, and a vent; see Figure C.4 for a schematic. Absorption can be monitored in a ﬂowing or static system. The entire setup is mounted onto a 2’ x 4’ optical breadboard, so that it is self-contained and can be easily moved to the shock tube end wall, or another experimental facility (i.e. another shock tube), with the only things required to reconnect are the tubes to the vacuum pumps, the inlet of the gas mixture, and the coaxial cables to the data-acquisition system.

Gas flow in from mixing assembly Multi-Pass Cell or shock tube

Baratron Vent

To pump

Figure C.4: Gas ﬂow diagram of the multi-pass cell setup.

The alignment procedure described in this section typically took the author one to two hours to complete from scratch if none of the optics were in place. Realignment typically took less than 30 minutes if the optics were setup but had become misaligned (e.g. if the table got bumped, the laser was borrowed, etc.).

Laser Noise

A measurement of the laser intensity, over a span of 5 minutes, yields a drift of 3% in laser intensity fluctuation in five minutes, even using common-mode rejection (from an incident power measured off the reflection of the cell window) because the fraction of light reflected off the cell window is not constant. This amount of noise still C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 193

leads to species mole fraction measurements with an uncertainty of 4% if the conditions are chosen as such to yield 50% absorption. Figure C.5 shows the dependence of the uncertainty in the measured mole fraction as a function of the percent absorption, illustrating that higher uncertainties are present at lower absorption levels. The uncertainty in the measured mole fraction is determined by propagating a 3% uncertainty in incident laser intensity into the Beer-Lambert law, Eq. 2.1. Because the laser noise contributes a random error, the overall uncertainty can be reduced by repeated measurements of the same parameter.

100 0 I

0.1

fraction due to a 3% uncertainty in 0.01 Percent error in measurement of mole- 0 102030405060708090100 % Absorption

Figure C.5: Uncertainty in the measured mole fraction using an absorption diagnostic with a 3% uncertainty in laser intensity. The uncertainty is shown a function of the percent absorption, illustrating that higher uncertainties are present at lower absorption levels.

Cell Length Calibration using Propane Mixture

The length of the multi-pass cell was checked with a 0.1% propane in argon mixture, prepared manometrically in the mixing tank. Because propane is naturally in the gas phase at room temperature, there is no concern of it adsorbing on the walls, and the manometrically predicted mole fraction is likely accurate. The 0.1% propane in argon mixture was introduced into the cell at pressures yielding 30 to 60% absorption, both in static and ﬂowing conditions. An absorption cross-section for propane from 194 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER

Klingbeil et al. [53] was used in determining the absorbing path length using the Beer-Lamber law, Eq. 2.1, assuming a known propane concentration. The cell length was measured to match the manufacturers specified length of 29.87 m within ±3% (measurements from 28.9 to 31.0 m were found). This fluctuation in cell length measurement is likely due to the fluctuations in the laser intensity. Because the scatter of all the measurements center on the manufacturers specified length, that length will be used in future measurements.

Measurements of n-Heptane Composition

A mixture of 200 ppm n-heptane in argon was prepared with the same double-dilution mixing procedure as used for the n-heptane experiments as described in Chapter 2, with the exception of no added TBHP. The mixture was introduced into the multi-pass cell from the mixing tank at pressures to ﬁeld 30 to 80% absorption. An absorption cross-section for n-heptane from Klingbeil et al. [53] was used in determining the n-heptane mole fraction. The measurements of heptane mole fraction scatter from 196 ppm to 207 ppm. This measurement conﬁrms the manometric preparation of n- heptane in an n-heptane/argon mixture within the ±3% of scatter, which is attributed to the laser noise. Other major independent uncertainties in the measurement include absorption cross-section (3% uncertainty), and path length (3% uncertainty), and if each of these major uncertainties are combined using a root-sum-squares method, the total uncertainty of n-heptane mole fraction is ±5%.

Measurements of TBHP Absorption Cross-section

A 50 ppm TBHP/water solution vapor in argon mixture was prepared (using the TBHP/water solution described in Chapter 2), and absorption at 3.39 µm was measured for 10-25% absorption. The amount of absorption was limited because the cell was ﬁlled to 1 atm at ∼25% absorption, therefore no higher absorption could be generated. This low concentration of TBHP/water in argon was chosen because it is the concentration used in the mixtures prepared for the work of this thesis. To minimize uncertainty in the measurement of absorption cross-section at 3.39 µm, multiple C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 195

absorption measurements at various pressures were performed.

A plot of ln(I/I0)/(x · L), normalized for units, versus pressure gives an absorption cross-section slope of approximately 2 m. This plot is shown in Figure C.6. If the TBHP yields are assumed to be the same as in measured in Chapter 3 (of approximately 12 ppm TBHP per 50 ppm TBHP/water solution), the measured absorption cross-section corresponds to a TBHP absorption cross-section at 3.39 µm of 8.3 m2/mole. This is ∼30% lower than the absorption cross-section of tert-butanol at 3.39 µm from Sharpe et al. [54], which has a similar molecular structure with TBHP (same number and type of C-H bonds). The uncertainty in the TBHP absorption cross-section measurement is approximately ±15%, however, because the amount of TBHP in each mixture is small compared to the amount of n-alkane or butanol in the mixtures prepared for pseudo-ﬁrst-order kinetics (by a factor of 10 to 20), this large uncertainty in absorption cross-section for TBHP only propagates into a ∼1% uncertainty in the fuel mole fraction measurements.

2.5

2.0 ) L 1.5 x / (

) 0 I

/ 1.0 I

-ln ( y = 1.95 x 0.5 [see caption for units]

0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Pressure [atm]

Figure C.6: Absorption measurements at various pressures of the 50 ppm TBHP/water in argon mixture. Units are normalized such that the slope gives absorption cross-section in units of m2/mole. 196 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER

Measurements of n-Heptane Composition in Mixture of n- Heptane/TBHP

A mixture of 50 ppm TBHP/water, 201 ppm heptane, and argon was prepared, and the heptane mole-fraction was measured by absorption at 3.39 µm in the multi-pass cell by assuming that the TBHP mole fraction and absorption cross-section were known (using the measured absorption cross-section value from the previous section). Ten measurements were done at total absorbances of 20 to 80%, and the average mole- fraction value measured was 201.6 ppm, with a deviation of ±3%. This deviation is an indication of the uncertainty due to baseline ﬂuctuations, and the only other major source of error is the n-heptane absorption cross-section, taken to be 3%, and if these major uncertainties are combined using a root-sum-squares method, the total uncertainty in the n-heptane mole fraction in a mixture in the presence of TBHP is ±5%. Since for similar mixtures of n-pentane and n-nonane, the same mixing procedure was used and the partial pressure of the n-alkane never exceeded more than 50% of its saturated vapor pressure (as was the case for the n-heptane mixtures), and the main diﬀerence in these molecules is only molecular weight and vapor pressure, similar uncertainties in fuel mole fraction can be assumed for those mixtures as well. Absorption measurements for those mixtures could be performed; however, because the cross-sections for those n-alkanes are less well known, the uncertainties in the measurements would be greater. Measurements of mixture composition in the shock tube was not done because passivation experiments have shown that no loss is found in the shock tube. Addi- tionally, the measurements of n-butanol in the following subsection show that no loss is expected in the shock tube.

Measurements of n-Butanol Composition

Because alcohols may have diﬀerent interactions with walls and/or TBHP because of the presence of a dipole (compared to no dipoles in n-alkanes), measurements of the n-butanol mole fraction in mixtures prepared according to the double-dilution mixing C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 197

procedure from Chapter 2 were conducted. Even though passivation experiments have eliminated most of the worry about any fuel condensing or adsorbing to the shock tube wall surfaces, recent ignition delay time experiments of n-butanol by Stranic et al. [35] in the same facility and similar shock tube facilities found evidence of n- butanol loss to wall surfaces. Therefore, the possibility of n-butanol loss to the shock tube walls was examined as well by filling the cell both directly through the mixing facility, and also by filling the cell by first filling the mixture into the shock tube, and then filling the cell through a port 2 cm from the shock tube endwall. A mixture of 190 ppm n-butanol in argon was prepared, and absorption of 3.39 µm was measured in the multi-pass cell. The absorption cross-section for n-butanol was taken from Sharpe et al. [54]. The results yield an n-butanol mole fraction measurement of 180 ppm when filling both from the mixing tank, and 181 from the shock tube endwall (with fluctuations of ±3%). This seems to indicate that the mixture in the shock tube is the same as that coming out of the mixing tank, but also that the measured mole fraction in both cases is low by 5%. However, recent unpublished measurements by Stranic [137] of the n-butanol absorption cross-section yield a cross-section that is approximately 4% lower than the value from Sharpe et al. If the measured absorption cross-section from Stranic is used, the measured n-butanol mole fraction in the mixture is 188 ppm, which is only 1% lower than the manometrically- prepared predicted amount. Because the absorption cross-section of n-butanol likely does not have an accuracy to better than 1%, the uncertainty of the n-butanol mole fraction is equal to that of the absorption cross-section combined with the measurement fluctuations (±3%), leading to an overall uncertainty in n-butanol mole fraction of ±5%, the same as for the n-alkanes. A mixture of 203 ppm n-butanol, 50 ppm TBHP/water and argon was also prepared and absorption was measured at 3.39 µm was measured in the multi-pass cell, filling from the mixing tank. The TBHP mole fraction and absorption cross-section were taken to be known, and the measured n-butanol mole-fraction using the n- butanol absorption cross-section from Stranic [137] was 207 ppm, with a measurement scatter of ±3%. Because the uncertainty of this measurement also includes the uncertainty of the TBHP absorption cross-section, the n-butanol mole fraction 198 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER

can be assumed to be veriﬁed within 3% in the presence of TBHP. Because the measured value for this mixture is higher than the manometric prediction, and the measured mole fraction in the previous n-butanol and argon mixture was lower than the manometrically predicted, this does not point to any sort of systematic error in the absorption cross-section of n-butanol at 3.39 µm, and the deviation of the measurements from the manometrically prepared predicted values are likely due to scatter in the measurements. For the same reasons as why absorption measurements in mixtures of n-pentane and n-nonane were not performed, absorption measurements in mixtures of the other butanol isomers were not performed, and similar uncertainties will be assumed. Be- cause both the n-heptane and n-butanol measurements provided similar uncertainties for fuel mole fraction, it seems reasonable that the other fuels would behave similarly. Appendix D

Rate Constant Estimation Methods

D.1 Introduction

In the past few decades, Sidney Benson’s additivity rules [138] have been important for estimating molecular heats of formation for large molecules using the principle that individual groups of atoms behave similarly in diﬀerent molecules. In addition to estimating thermochemical properties, the additivity principle also has applications in estimation of kinetics rate constants. For the class of reactions of the hydrogen-atom- abstraction-by-OH type, predictive models for the rate constants using the additivity principle based on structure-activity relationships have been investigated and improved in the past few decades. Several diﬀerent types of rate constant estimation methods will be discussed in this appendix, including details on how to apply them to estimate the rate constants for the reactions investigated in this thesis.

Deﬁnitions

A few common terms will be used to succinctly describe the estimation methods discussed in this appendix. The terms primary, secondary, and tertiary are used to distinguish diﬀerent types of carbons in an organic molecule.

199 200 APPENDIX D. RATE CONSTANT ESTIMATION METHODS

• Primary carbon: a carbon atom bonded to only one other non-hydrogen atom. A primary carbon is bonded to three hydrogen atoms. • Secondary carbon: a carbon atom bonded to two other non-hydrogen atoms. A secondary carbon is bonded to two hydrogen atoms. • Tertiary carbon: a carbon atom bonded to three other non-hydrogen atoms. A tertiary carbon is bonded to only one hydrogen atom.

In this thesis, the non-hydrogen atoms are typically carbon, except in the case of butanol, where the an oxygen atom may take the place of a non-hydrogen atom. For butanol molecules, the carbon atoms can also be distinguished by their position relative to the oxygen atom.

• α-Carbon: the carbon atom adjacent to the oxygen atom. • β-Carbon: the second carbon atom from the oxygen atom. • γ-Carbon: the third carbon atom from the oxygen atom. • δ-Carbon: the fourth carbon atom from the oxygen atom.

Primary, secondary, or tertiary carbons can also be diﬀerentiated by the neighboring groups. For example, in n-heptane, three secondary carbons exist. However, the central secondary carbon is bonded to two other secondary carbons, and the other secondary carbons are bonded to one primary carbon and one secondary carbon. In this appendix, a notation will be used similar to the notation used in Benson’s additivity rules [138].

• (CH3)–(CH2): a primary carbon bonded to a secondary carbon.

• (CH2)–(CH3)(CH2): a secondary carbon bonded to a primary carbon and a secondary carbon.

• (CH2)–(CH2)(CH2): a secondary carbon bonded to two secondary carbons.

• (CH2)–(CH2)(OH): a secondary carbon bonded to a secondary carbon and an OH group.

• (CH)–(CH2)(CH2)(CH2): a tertiary carbon bonded to three secondary carbons. • and so on...

The neighboring groups on the right-hand side of the long hyphen will also be referred to as substituent groups. D.2. EMPIRICAL ESTIMATION METHODS 201

Figure D.1 shows the n-heptane and iso-butanol molecules and uses the above terminology to describe each carbon atom.

Secondary carbon (CH ) - (CH )(CH ) 2 3 2 Tertiary carbon CH β 3 -carbon Hydroxyl group H H H2 2 2 (CH) - (CH3)(CH3)(CH2) C C C CH OH (OH) - (CH2) Primary carbon (CH3) - (CH2) H C C C CH H C C 3 3 3 Secondary carbon H2 H2 H2 Primary carbon α-carbon Secondary carbon γ-carbon (CH2) - (CH)(OH) (CH2) - (CH2)(CH2) (CH3) - (CH)

Figure D.1: The carbons of the n-heptane (left) and iso-butanol (right) molecules described using the terminology used in this appendix.

D.2 Empirical Estimation Methods

Early Models Not Discussed in this Thesis

Greiner [19] (1970) presented data for hydrogen-atom abstraction by OH of ten different model alkanes, and used this data to generate a simple additivity model for the kinetic rate constants, analogous to Benson’s model [138] for thermodynamic quantities. All of Greiner’s experiments were for temperatures from 295 to 500 K. The overall rate constant predicted for any alkane+OH reaction is a function of the number of primary, secondary, and tertiary carbons present in the alkane, and given by Eq. D.1, where NP , NS, NT are the number of primary, secondary, and tertiary carbons in the alkane, respectively.

! 818 k /[cm3molecule−1s−1] =1.02 × 10−12 · N · exp − tot P T [K] ! 403 + 2.34 × 10−12 · N · exp − S T [K] ! 95 + 2.09 × 10−12 · N · exp + (Eq. D.1) T T [K] 202 APPENDIX D. RATE CONSTANT ESTIMATION METHODS

Greiner found that his model worked well with his data for neo-pentane, 2,2,3,3-trimethhylbutane, pentane, n-butane, cyclohexane, n-octane, iso-butane, 2,3-dimethylbutane, 2,2,3-trimethylbutane, and 2,2,4-trimethylpentane. However, Greiner found the abstraction rate with methane and ethane did not agree well with his model.

Baldwin and Walker [23] (1979) proposed an additivity method for the rate constants for reactions of alkanes+OH, depending on the number of primary, secondary, and tertiary carbons, similar to Greiner [19]. The model of Baldwin and Walker is based on their data taken at 500 ◦C combined with independent data at lower temperatures. The overall rate constant is given relative to the rate constant of

OH + H2 −→ H2O + H as Eq. D.2. ! ! 1070 1820 k /k = 0.214 · N · exp + 0.173 · N · exp tot ref P T [K] S T [K] ! 2060 + 0.273 · N · exp − (Eq. D.2) T T [K]

In Eq. D.2, kref is the rate constant for the reaction of OH+H2 −→ H2O+H. Baldwin and Walker also proposed a relative rate constant expression to determine the overall rate constants for reactions of alkanes+H.

In a subsequent paper, Walker [139] (1985) used reliable experimental data at room temperature and 753 K to develop an additivity model for the rate of alkanes+OH, presenting speciﬁc rate constant contributions for each abstraction site dependent on the next-nearest neighbor (NNN) of the C–H bond. The experimental rate constant evidence supports a pre-exponential rate constant temperature dependence based on T 1. Walker’s recommended rate constant contributions are given in Table D.1. Using Walker’s additivity method, rate constant agreement with the limited amount of experimental data available at the time was found to be very good, though the paper cautions that steric eﬀects may limit this approach and the approach of similar additivity methods on highly branched alkanes. D.2. EMPIRICAL ESTIMATION METHODS 203

Table D.1: Group rate constants recommended by Walker [139]. Units for k are [cm3molecule−1s−1].

Carbon type at abstraction site Rate constant contribution per H atom −15 (CH3) (neopentane) k = 5.81 × 10 T exp(−605/T [K]) −15 (CH3) (tetramethylbutane) k = 2.32 × 10 T exp(−404/T [K]) −15 (CH2)–(CH3)(CH3) k = 4.82 × 10 T exp(−130/T [K]) −15 (CH2)–(CH3)(CH2) k = 4.82 × 10 T exp(−60.1/T [K]) −15 (CH2)–(CH2)(CH2) k = 4.82 × 10 T exp(+10.8/T [K]) −15 (CH2)–(CH2)(CH) k = 4.82 × 10 T exp(+10.8/T [K]) −15 (CH)–(CH3)(CH3)(CH3) k = 4.48 × 10 T exp(+75/T [K]) −15 (CH)–(CH3)(CH3)(CH2) k = 4.23 × 10 T exp(+160/T [K]) −15 (CH)–(CH3)(CH3)(CH) k = 3.99 × 10 T exp(+245/T [K]) −15 (CH)–(CH3)(CH3)(C) k = 3.65 × 10 T exp(+330/T [K]) −15 (CH)–(CH3)(CH2)(CH2) k = 3.99 × 10 T exp(+245/T [K])

Structure-activity Relationship of Atkinson and Coworkers

Atkinson [20] (1986) makes high-temperature rate constant estimations (250 to 1000 K) for reactions of OH with alkanes, haloalkanes, oxygenates, nitriles and ni- trates. Atkinson’s model distinguished carbon sites with different neighboring groups, rather than assuming all primary, secondary, and tertiary reaction sites were equivalent between molecules. For alkanes, Atkinson’s defines a rate constant for the hydrogen-atom abstraction via OH based on a structure-activity relationship, and the estimated rate constant can be calculated with rates for each of the primary, secondary, and tertiary carbons with F (X) factors for each substituent group. The overall rate constant can be defined by Eq. D.3, where Fi(X) is a factor dependent on the neighboring group(s) X, Y , and Z of the primary, secondary, and tertiary carbons for each carbon i, and kp, ks, and kt are terms for the rate constant contributions at primary, secondary, and tertiary carbon sites, respectively.

N N N XP XS XT ktot = kpFi(X) + ksFi(X)Fi(Y ) + kpFi(X)Fi(Y )Fi(Z) (Eq. D.3) i=1 i=1 i=1

Each substituent factor term can be written in the temperature-dependent form of Eq. D.4, eﬀectively lowering the activation energy of each associated rate constant 204 APPENDIX D. RATE CONSTANT ESTIMATION METHODS

term. ! E F (X) = exp x (Eq. D.4) T

Atkinson used data to recommend the F (X) factors for alkanes. Atkinson also recommended F (X) factors for molecules containing oxygen, nitrogen and halogen molecules. For example, the hydrogen-atom abstraction rates via OH of alcohols can be estimated with the F (OH) factor.

Atkinson’s [20] approach was later revisited by Atkinson and co-workers [21, 22, 90] (1987,1995,2001), generating an improved database of rate constants, and suggested factors for new substituent groups, and updating the factors for the same previous groups. The most recent relevant rate constants are from Kwok and Atkinson [22] (1995), and are described by Eq. D.5, Eq. D.6, and Eq. D.7; these terms can be substituted into Eq. D.3. For alcohols, Eq. D.8 adds an additional term to Eq. D.3 that can be aﬀected by substituent factors.

! 320 k = 4.49 × 10−18T 2 exp − cm3molecule−1s−1 (Eq. D.5) p T [K] ! 253 k = 4.50 × 10−18T 2 exp + cm3molecule−1s−1 (Eq. D.6) s T [K] ! 696 k = 1.89 × 10−18T 2 exp − cm3molecule−1s−1 (Eq. D.7) t T [K] ! 85 k = 2.10 × 10−18T 2 exp − cm3molecule−1s−1 (Eq. D.8) oh T [K]

The most recent F (X) factors for alkanes are also from Kwok and Atkinson, and Bethel et al. [90] (2001) studied the rate constants for reactions of selected diols with OH to determined updated substituent factors for alcohol-related substituent groups. Eq. D.9, Eq. D.10, and Eq. D.11 extrapolate the new substituent factors proposed at D.2. EMPIRICAL ESTIMATION METHODS 205

298 K by using Eq. D.4.

! 61.69 F (CH ) = F (CH) = F (C) = exp (Eq. D.9) 2 T [K] ! 317.3 F (OH) = exp (Eq. D.10) T [K] ! 284.7 F (CH OH) = F (CHOH) = F (COH) = exp (Eq. D.11) 2 T [K]

Bethel et al. found that for hydroxyl-containing compounds, the substituent group eﬀect of the OH group needed to be considered at both the α-carbon and the β- carbon, as suggested by Eq. D.11. The substituent group for a neighboring primary carbon is one, F (CH3) = 1.

The structure-activity relationship (SAR) from Atkinson and coworkers [20–22, 90] can be used to estimate the overall rate constants for the reactions of interest in this thesis. For example, the rate constant for the reaction of OH with n-heptane, Reaction (4.2) can be computed using Eq. D.12, and the rate constant for the reaction of OH with iso-butanol, Reaction (6.1), can be computed using Eq. D.13.

SAR k4.2 = 2kpF (CH2) + 2ksF (CH2) + 3ksF (CH2)F (CH2) (Eq. D.12) SAR k6.1 = 2kpF (CH) + ktF (CH2OH) + ksF (CH)F (OH) + kohF (CH2) (Eq. D.13)

Furthermore, site-speciﬁc rate constants can be estimated by examining the rate constant term and substituent factor associated with each individual carbon site. For example, abstraction at the β-carbon of iso-butanol, Reaction (6.1b), can be described by the rate constant term associated with the tertiary carbon site, given by Eq. D.14

SAR k6.1b = ktF (CH2OH) (Eq. D.14)

See Figure D.1 for the molecular structures and types of carbon abstraction sites for n-heptane and iso-butanol. 206 APPENDIX D. RATE CONSTANT ESTIMATION METHODS

Improved Group Scheme of Sivaramakrishnan and Michael

The most recent development for an additive group scheme for the reaction rate of OH with alkanes is from Sivaramakrishnan and Michael [11] (2009). Sivaramakrishnan and Michael measured the rate constants for reactions of OH with alkanes up to

C7, and used the resulting experimental data to deduce the rates of abstraction from primary, secondary, and tertiary carbon sites diﬀerentiated similarly to Walker’s next- nearest neighbor (NNN) distinctions [139].

Motivated by high-level energetics calculations for bond energies, Sivaramakrish- nan and Michael [11] also used their rate constant measurement results for their largest normal alkane (n-heptane) to diﬀerentiate the abstraction rate constant at secondary carbon sites even more, and accounted for eﬀectively the next-next-nearest neighbor. For example, in the n-heptane molecule shown in Figure D.1, the central secondary carbon (CH2)–(CH2)(CH2) is bonded to two secondary carbons that are both bonded to secondary carbons (they call this carbon S11’); however, the outer secondary carbons (CH2)–(CH2)(CH2) are bonded to one secondary carbon that is bonded to a secondary carbon and one secondary carbon bonded to a primary carbon

(they call this carbon S’11).

Using their experimental data, Sivaramakrishnan and Michael [11] came up with empirical rate constant parameters for each type of carbon site, and their improved group scheme successfully predicts the n-octane+OH rate constant measured by Kof- fend and Cohen [9] near 1100 K. All rate constant ﬁts were determined for experimental data in the temperature range 298 to 1300 K. The rate constants terms for Sivaramakrishnan and Michael’s improved group scheme additivity method are given in Table D.2.

The improved group scheme by Sivaramakrishnan and Michael [11] can be used to estimate the rate constants for the reactions of OH with n-pentane, n-heptane, and n-nonane, Reaction (4.1), (4.2), and 4.3, respectively, that were studied in this thesis. Eq. D.15, Eq. D.16, and Eq. D.17 use the improved group scheme to estimate D.3. TRANSITION STATE THEORY 207

the rate constants of interest in this thesis.

kIGS = 2k + 2k + k (Eq. D.15) 4.1 (CH3)−(CH2) (CH2)−(CH3)(CH2) (CH2)−(CH2)(CH2)(S11) kIGS = 2k + 2k + 2k 4.2 (CH3)−(CH2) (CH2)−(CH3)(CH2) (CH2)−(CH2)(CH2)(S11) + k (Eq. D.16) (CH2)−(CH2)(CH2)(S11’) kIGS = 2k + 2k + 2k 4.3 (CH3)−(CH2) (CH2)−(CH3)(CH2) (CH2)−(CH2)(CH2)(S11) + 3k (Eq. D.17) (CH2)−(CH2)(CH2)(S11’)

Table D.2: Improved group scheme rate constant terms recommended by Sivaramakrishnan and Michael [11]. Units for k are [cm3molecule−1s−1].

Carbon type at abstraction site Rate constant contribution per H atom −18 1.813 (CH3)–(CH2) k = 7.560 × 10 T exp(−437/T [K]) −18 2.078 (CH3)–(CH) k = 9.267 × 10 T exp(−189/T [K]) −18 1.763 (CH3)–(C) k = 9.087 × 10 T exp(−374/T [K]) −17 1.751 (CH2)–(CH3)(CH3) k = 1.640 × 10 T exp(+32/T [K]) −15 0.935 (CH2)–(CH3)(CH2) k = 5.856 × 10 T exp(−254/T [K]) −18 1.811 (CH2)–(CH2)(CH2) (S11) k = 4.750 × 10 T exp(+511/T [K]) −13 0.320 (CH2)–(CH2)(CH2) (S11’) k = 4.665 × 10 T exp(−426/T [K]) −18 1.840 (CH)–(CH3)(CH3)(CH3) k = 8.044 × 10 T exp(+503/T [K]) −14 0.320 (CH)–(CH3)(CH3)(CH) k = 7.841 × 10 T exp(+35/T [K])

D.3 Transition State Theory

Cohen [24, 25] (1982,1991) developed a method for extrapolating existing experimental data on the rate constants for reactions of OH radicals with alkanes to higher temperatures using conventional transition-state theory (TST). In Cohen’s earlier work [24], all primary, secondary, and tertiary carbon abstraction sites were treated the same in different alkanes. However, in a later development [25], Cohen revised the transition-state theory model to include differences in contributions from each primary, secondary, and tertiary carbon abstraction site due to the next-nearest neighbor (NNN). The NNN contribute to bond dissociation energy differences which effects the 208 APPENDIX D. RATE CONSTANT ESTIMATION METHODS

enthalpy of the transition state. In the revision of Cohen’s theory, Cohen also examined the affect in extrapolating the rate constant estimation method to large alkanes due to increased mass. Cohen’s conclusion was that mass differences may possibly affect the transition state entropy by up to 40%, which can introduce a factor of 2 error in rate constant. However, because the current experimental database for rate constants for reactions of OH with large-alkanes is too small and the experimental uncertainties too large, Cohen was unable to unambiguously distinguish the affect of mass in the model.

D.4 Ab initio Prediction Methods

Alternative to empirical additivity methods are ab initio prediction methods that utilize some form of ab initio calculation but do not require full electronic-structure calculations for high-level rate constant calculations. Rate constants using these methods are not discussed in comparison to the results of this thesis. Huynh et al. [26] (2006) applies reaction class transition state theory (RC-TST) to predict thermal rate constants for the hydrogen-atom abstraction reactions of the type alkane+OH. Using the RC-TST coupled with linear energy relationships (LER), Huynh et al. were able to predict relative rates in the alkane+OH reaction class (relative to ethane+OH) with knowledge only of the reaction barrier height for the general alkane reaction, which can be obtained using electronic structure calculations. The RC-TST/LER rate theory by Huynh et al. is shown to have reasonable agreement with literature rate values for a large number of reactions in this reaction class. Sumathi and co-workers [140] (2001,2003) claim that while estimation methods based on linear free energy relationships have been known for a long time, the draw- backs of the LER theories can include thermodynamic inconsistency, missing information about Arrhenius factors or lack of universality. Instead, the approach on group additivity by Sumathi et al. [140] is to calculate thermodynamic properties of transition states based on ab initio calculations to extract group additivity values for “transition-state speciﬁc” moities. However, this work is done only for hydrogen-atom D.4. AB INITIO PREDICTION METHODS 209

abstraction from alkanes by H and CH3 radicals, and no work is reported regarding abstraction by OH. Other hydrogen-atom abstraction rates from oxygenates, oxyalkyls and alkoxycarbonyls were studied by Sumathi and Green [141], however, this work also only covers abstraction by H and CH3 radicals. 210 APPENDIX D. RATE CONSTANT ESTIMATION METHODS Appendix E

Estimation of Rate Constants for Unimolecular Reactions

E.1 Introduction

Two main types of unimolecular reactions are discussed in this thesis as important subsequent reactions that occur after the reaction of OH with the isomers of butanol. beta-Scission reactions are an important class of reactions that lead to decomposition of free radicals. This type of reaction describes the decomposition of a free radical breaking at the bond β to the radical, meaning two bonds away from the radical. The β-bond is the bond most likely to break because breaking of this bond allows for the formation of a double bond. Typically, beta-scission through breaking of a C–C bond or a C–O bond will occur more rapidly than cleavage of a C–H or O–H bond because the latter pair of bonds are stronger. See Figure E.1 for an arrow pushing diagram of a beta-scission reaction. Radical isomerization can occur through unimolecular reactions. This type of reaction typically occurs through a transition state structure where a hydrogen atom is exchanged from one carbon (or oxygen) site to a radical site. The fastest isomerization reactions to consider for butanol are ones that occur via a 5- or 6-membered ring transition state structure (see Figure E.2). Smaller ring transition state structures are not likely to occur, therefore, isomerization reactions that pass through these

211 212 APPENDIX E. RATE CONSTANTS FOR UNIMOLECULAR REACTIONS

types of structures are not likely to occur on combustion time scales.

Three beta-scission decomposition pathways of the 1-hydroxy-but-2-yl radical

H H H H H2 H C C C CH2 C C OH H3C C OH H H H H

H H H H H2 H2C C H C C C CH3 C OH C OH H H H H

H H H H H H H2 C C H C C slow H3C C OH C C OH H H H H Figure E.1: Three beta-scission decomposition pathways for the 1-hydroxy-but-2-yl radical. Red arrows show the movement of electrons. Also shown in red is the free radical and the bond in the β-position relative to the free radical involved in each reaction.

1-hydroxy-but-4-yl 1-butoxyl

H2 H2 6-member-ring TS H2 H2 C C C C H2C C OH H3C C O H2 H2C H2 C O H2 H H2C C H

1-hydroxy-but-3-yl 1-butoxyl

H H2 5-member-ring TS H2 H2 C C C C H3C C OH H3C C O H2 H H2 H C C 3 C O H2 HC H

Figure E.2: Isomerization reactions for C4H9O radicals. Example reactions proceeding through 6- and 5-member ring transition states are shown.

At high pressures, the rate constants for unimolecular reactions are only dependent on temperature. All unimolecular reactions, however, necessarily proceed via collision with a third body, and therefore, at lower pressures, the rate constant for a given unimolecular reaction is dependent on the concentration of third body collision partners. Thus, rate constants for unimolecular reactions can be pressure dependent in addition to temperature dependent. Several methods are available for predicting the pressure dependence of a unimolecular reaction; methods can be as complex as E.2. HIGH-PRESSURE LIMIT 213

requiring high-level electronic structure calculations to determine the vibrational fre- quencies of the reactants and transition states, or as simple as assuming the reaction proceeds via a two-step Lindemann mechanism [99]. The work in this thesis takes an approach with a complexity between these limits. In this appendix, a method for determining the high-pressure limit rate constant for beta-scission unimolecular reactions will be presented based on the examination of analogous reactions. Furthermore, the methods of estimating the pressure dependence of unimolecular reactions using the Kassel Integral [99] will be described.

E.2 High-pressure Limit

In Chapter 5, the high-pressure limit of the rate constants for reactions describing beta-scission decomposition of the C4H9O radicals were estimated based on the reverse addition reaction, a method described in Curran [100] for similar decomposition reactions of alkyl and alkoxyl radicals. The rate constants for the addition reactions can be estimated by assuming that addition reactions with similar molecular interactions have equivalent reaction rate constants. This assumption was made on the basis of Figure E.3 which shows measured rate constants for addition reactions of alkene+CH3 and alkene+OH from Manion et al. [142]. For example, the reverse of Reaction (5.4a): CH3CH2CHCH2OH −→ 1- C4H8 + OH is the addition of an OH radical with a 1-butene molecule, and the rate constant for such a reaction can be estimated to be equivalent to the addition reaction of an OH radical with a propene molecule to form a hydroxypropyl radical product. The rate constants for the latter reaction and other classes of addition reactions, can be determined from applying the law of mass action to the work of Z´ador and Miller [93], who performed ab initio calculations on the unimolecular pathways for the decomposition of hydroxypropyl radicals. In the current work, the assumption was made that calculated rate constants at 100 bar are representative of the high-pressure limit rate constant. Thermodynamic properties were taken from Sarathy et al. [91] in calculating the reverse rate constants. Table E.1 presents the families of addition reactions and the rate constants assumed for each using this method. 214 APPENDIX E. RATE CONSTANTS FOR UNIMOLECULAR REACTIONS

10-9 -10 10 OH + alkenes 10-11 -12 Alkene type: 10 1 ]

-1 -13 C s 10 2 -1 C -14 3 10 iso-C 4

-15 10 n-C 4 -16 C 10 2 -17 C 10 3

[cm3molecule -18 CH + alkenes 10 3 10-19 Recombination rate constant 10-20 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1000/T [1/K]

Figure E.3: Rate constants for addition reactions of alkene+CH3 and alkene+OH from Manion et al. [142].

Table E.1: Families of addition reactions with equivalent rate constants. High-pressure limit rate constants are determined from the work of Z´adorand Miller [93] using thermodynamic properties from Sarathy et al. [91]. Units for A are [cm3mol−1s−1] , units for E are [cal mol−1K−1].

b Addition Reaction k∞ = A · T exp(−E/RT ) A b E

1 3 C2H5 + CH2O −−→ CH3CH2CH2O 1.81×10 2.55 -3.533×10 1 3 C3H7 + CH2O −−→ CH3CH2CH2CH2O 1.81×10 2.55 -3.533×10 6 3 CH3 + CH2−CHOH −−→ CH3CH2CHOH 3.04×10 1.68 6.619×10 6 3 CH3 + CH2−CHCH2OH −−→ CH3CH2CHCH2OH 3.04×10 1.68 6.619×10 6 3 C2H5 + CH2−CHOH −−→ CH3CH2CH2CHOH 3.04×10 1.68 6.619×10 6 3 CH2OH + C3H6 −−→ CH3CHCH2CH2OH 3.04×10 1.68 6.619×10 7 3 OH + C3H6 −−→ CH3CHCH2OH 7.54×10 1.20 -1.705×10 7 3 OH + 1- C4H8 −−→ CH3CH2CHCH2OH 7.54×10 1.20 -1.705×10 6 3 CH2OH + C2H4 −−→ CH2CH2CH2OH 1.28×10 1.60 2.7767×10 6 3 2- C2H4OH + C2H4 −−→ CH2CH2CH2CH2OH 1.28×10 1.60 2.7767×10 E.3. FALL-OFF LIMIT 215

A similar method for estimating the high-pressure limit rate constant for beta- scission decomposition reactions relevant to tert-butanol radicals was done in Chap- ter 8. In that chapter, the assumption was made that the rate constant of the addition reaction of a methyl radical plus iso-butene is equivalent to the rate constant for the addition reaction of a methyl radical plus propen-2-ol, and the rate constant for the former reaction was taken from the work of Sun and Bozzelli [132].

E.3 Fall-oﬀ Limit

Because all of the experiments and simulations in this thesis were at pressures of 1 to 2 atm, the rate constants for the unimolecular reactions, including both the beta-scission and isomerization reactions of the C4H9O radicals, are likely not at the high-pressure limit. To determine the amount of rate constant fall off from the high- pressure limit rate constant, the Kassel Integral [99] is used, which is given by Eq. E.1, where k∞ is the high-pressure limit rate constant, S represents the effective number of oscillators, and B and D are defined by Eq. E.2 and Eq. E.3, respectively.

k 1 Z ∞ xS−1e−x = I(S,B,D) = D S−1 dx (Eq. E.1) k∞ Γ(S) 0 1 + 10 [x/(B + x)] E∗ B = (Eq. E.2) kT ν D = (Eq. E.3) k−1[M]

In Eq. E.2 and Eq. E.3, E∗ is the activation energy of the high-pressure limit rate constant, ν is the A-factor of the high-pressure limit rate constant, k−1 is the molecular collision frequency dependent on temperature and pressure, and [M] is the molecular gas concentration. The gamma function is Γ(S) = (S − 1)!. Estimation for the number of eﬀective oscillators can be made by assuming S = Smax/2, where Smax is the maximum number of vibrational modes, or a value of S can be chosen that leads the Kassel Integral to predict a relative pressure dependence determined using high- level electronic structure calculations. In the current work, the integral in Eq. E.1 was evaluated using a Riemann sum method that was designed to converge to the 216 APPENDIX E. RATE CONSTANTS FOR UNIMOLECULAR REACTIONS

correct value. For the beta-scission reactions, the Kassel Integral in Eq. E.1 is applied to the high- pressure limit rate constant in the endothermic (dissociation) direction. However, for the isomerization reactions, re-deriving the Kassel Integral using the same method as in Benson [99] yields the integral in Eq. E.4.

k 1 Z ∞ xS−1e−x = I(S,B,D) = D S−1 D0 0 S−1 dx k∞ Γ(S) 0 1 + 10 [x/(B + x)] + 10 [x/(B + x)] (Eq. E.4)

In Eq. E.4, D and B are calculated by Eq. E.2 and Eq. E.3, respectively, in any chosen forward direction of the isomerization reaction, and D0 and B0 are calculated by Eq. E.2 and Eq. E.3, respectively, in the corresponding reverse direction of the isomerization reaction. It was found for the isomerization reactions of interest in this thesis, Eq. E.4 is equivalent to Eq. E.1 applied to the isomerization reaction in the exothermic direction. Bibliography

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